Maths-
General
Easy
Question
Use the Law of Detachment to make a valid conclusion in the true situation.
If a number is odd, then its square is odd.
![x equals 7 text is odd end text](data:image/png;base64,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)
Hint:
Law of Detachment states that if p
q is true and it is given that p is true then we can conclude
that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.
The correct answer is: Hence, we can conclude that the square of the 7 is odd
Consider the statement into two separate statements
p: The number is odd
q: The square of the number is odd
So we can write the given statement “If two angles have the same measure, then they are congruent” as:
![p not stretchy rightwards arrow q](data:image/png;base64,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)
We are given
x = 7 is odd
which means the number is odd so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e. the square of 7 is odd.
Final Answer:
Hence, we can conclude that the square of the 7 is odd
Related Questions to study
Maths-
Show the conjecture is false by finding a counterexample. If a + b = 0, then a = b = 0.
Show the conjecture is false by finding a counterexample. If a + b = 0, then a = b = 0.
Maths-General
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Prove that ∠PRS ≅ ∠PSR
![](data:image/png;base64,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)
Prove that ∠PRS ≅ ∠PSR
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARYAAAC0CAYAAABR7gMeAAAgAElEQVR4nO2deVwV1fvHPzNzL4sbprihYgKuqaiBaWqa5papaWUCatbPzH3fMLXUvloI8nXNENPccN9Ks7Iy09JyKbevppkpoCiyw91m5vn9ce8Z5+IGCNx7Yd69CIS5M2dmznnOs57DERFBQ0NDoxDhHd0ADQ2NkocmWDQ0NAodTbBoaGgUOppg0dDQKHQ0waKhoVHoaIJFQ0Oj0NEEi8YjIfY/AkAEQLb+g+59k4hAJNv9TqN0owkWjYdCAESSQTKBzASIMgARgFWIkAyYZBlG2QSzZAEkAiRAJoKsiZdSjc7RDdBwbogDZHAQQJBlCWaTEaLEQUdukGWCZ3kPGKCHZJEgA+A5R7dYwxnQBIvGI+GIB8fJgI7w+6/HEfHfaNy9mwbIQMUK5fFi927o/dprqO5dxWoJcQRAky6lHc0U0ngkHACOI0CQcO3aFezcsRuVq9VCv/6vw2hMx4czZ+Lz1V9A0PHgBAJ4CaSZQaUeTbBoPBoCrA5bC3iBA68vixdf6obRo0ZiyeJI6HkBvx07DYNZhAQR4CRoHlwNTbBo5AGb05aXwUEPQe8BHkD5snoIPAdZ5gCeB8cRCJKjG6vhBGg+Fo08Qla7iOdw9co/OP7HH/hp/1akp2egSZPGcNfxsBlOtv80SjOaYNF4KFYxwWwaPXgOcOfN2Ph5LPbu3ALJlIF3h4/Au0P6QxBlCLwe4PTgNbFS6tEEi8YjuScieIA4kCzh5e5d8ELnjqhRzRutglqiQvnykCQJHMdrASENAJpg0cgTHAAeRBxkGWjbti0Gh74GALBYRJgtFuh0giZUNBQ0waLxSMjmWgEnQxQJOkEHUbJABMARoNMJICJwnCZVNO7BaUtTajwKSSJwnAgeIhITkvDnn5fQoHFj+NSpAT3PQXioQOGgqTClF02waDwSWSIQmcHzBE4WIJMeFlkGdCJ0PCBwD1N6NcFSmtHyWDQeDQdwvABZBoh4yCRDp+MgyzI4cCCSlS9rvgv70ijNaIJF45HwPMDzAnjBDRB4ECdDEDhs27INZ86cA8cJEEUZsgwAgupLozSjCRaNx2BLeuN4cDwHSbJgzZo1mBn+PsKnz8CNG/HgecG6VIti/mhmUGlHEywaeUYURWzYsBGzZ8/GzVs3cfDgQXz00Ue4c+cOdDotwKhxD603aNhBRFD784kIgiDAaDRaNZWZM5GSkoIpU6bg999/x/r16wEAERERqFChAiRJAhFBp9NpIehSjBYV0rCDiCBbHSbgOA48zyM7OxuLFy9GREQE0tPT0bx5c6xbtw5msxmdO3eGwWDAkCFDMHfuXFSrVg0mkwlubm6aYCnFaKaQxgORZRkcxyEtLQ0rVqzA/PnzYTAY4Obmhvfeew+NGjVCo0aN8PLLL8NsNmPt2rWIjIxEUlKSJlA0NMGiYYWZQEyB1ev1SEpKwty5czFr1iyYTCaYzWa0atUKHTt2hCAI8PDwwMiRI1G7dm1YLBZERUXho48+QlZWFjiOu++cGqUHTbBoKOYP+xIEAdeuXcPs2bOxYsUK6PV6SJKESpUqYeDAgQgICFB8KS1atMAbb7wBHx8fNGrUCGvWrMHcuXORnp4OAJAkCbIsa8KllKEJFg27wS8IAi5duoSpU6di3bp1qFmzJnx9fUFECAoKQu/evcHz1m7DcRzKli2Lfv36oW7dunjjjTfQpk0bfPrpp/jggw9w584du2M1Sg+aYNEAz/MQBAE8z+PSpUuYOHEitm/fDh8fH0ycOBF3796Fl5cX+vTpgxo1aijahyiKkGUZzz77LDp37oxr165h1qxZaNu2LWJjYxEREYGcnBwIgpYwV9rQBEsphIggSZJizjBBcebMGYwdOxb79+9HUFAQPvvsM1y4cAHJycno3r07hgwZohzL8zz0ej2ICB4eHnj11Vdx5coV3Lp1CzExMWjbti2WL1+OyZMn4+7duwBgd02Nko0mWEopzDRhSx6cOnUKY8aMwXfffYe2bdsiJiYGOp0OO3fuRPny5REaGgpPT09wHKdoN+xnAGjatCk6duyIffv2oWLFili9ejW6dOmCdevW4eOPP0Z6ejoEQVBC2RolHNIolUiSRKIokiiK9P3331PDhg0JAPXo0YPOnj1LRqORQkJCSKfT0eDBgykzM5MkSXrkOW/cuEHdu3enDRs2kCzLdO3aNQoNDaUKFSrQzJkzKSUlhWRZJlmWi+kuNRyFJlhKCWxAS5JEkiQpg3vbtm3UpEkTAkADBgygc+fOERHRpk2bqEqVKuTt7U1nzpxRBNGjzk9EFBkZSb1796a0tDQiIkpKSqKhQ4eSl5cXTZkyhYxGo117NEommmApJTDtxGQykcViIZPJRNu3b6eAgADS6/U0dOhQunr1KhERxcfHU/fu3QkAjRs3TvnMozQWWZZJFEVKTEyk7t27U1xcnCI4bt68SaNGjSJvb2+aPn06paamkiRJZDabSRRFTcCUQDTBUkoQRZHMZjNZLBYyGAy0fv16ql27Nun1epo4cSLdvn2bRFEki8VCa9asoYoVK1KTJk3o7NmzipbzOMFiMplIkiTasGEDtW/fnm7cuKFoJikpKTRlyhQqX748TZs2jVJTU0kUxceaVxquiSZYSglMMGRlZdHy5cupatWqVK5cOfrkk08oOTmZiIjMZjOdPXuW2rVrRwAoMjKSzGYzybKsfH8YTBsym82UnJxMXbp0oeXLlyvnJSK6e/cuLViwgKpXr05TpkyhrKysor9xDYegCZYSDDNPmLmRnp5OERERVKlSJfL29qaFCxdSenq64nMRRZGioqIIALVq1YrOnz9PRKR8/lGChflv2HFff/019ezZUzGvmGZiMBho3rx55OvrS1OnTqWMjAySZZksFotmFpUgNMFSQmFaBjM3UlJSaOHChaTT6cjHx4eWLFlCJpNJOY6I6Pz58/Tss8+Su7s7xcbGKucpCKmpqTR48GCaNWvWfULJYDBQVFQU1axZkz766CNKS0sjs9lMBoNBEywlBE2wlFCYFkBkjcxMnDiR3N3dqW7durRx40YlymM2m0mSJMrJyaGpU6cSAOrUqRNdvnz5iSI3oijSrl27qFu3bnTx4sX7/m40GikmJob8/f1p1qxZlJGRobRbw/XRBEsJg5kc7HtiYiINHz6c9Ho9PfPMM7R9+3ZFmDCfiCzLdObMGapduzZVqVKFYmNjn9g0kWWZUlNTafLkyTR37lxFO2KmmSRJZDQaae3atdS0aVOaNWsW5eTkKJ/VBIxro2XeliBYMaEsy+B5Hn///TfCw8Px2WefoVatWli0aBFeffVVpTCQ53llIaeIiAgkJiaiffv2ePPNN5VjCoosy6hYsSK6deuGkydP4uzZs+A46+r+LLVfEARUqlQJlStXxqpVq5QMXVEUYbFYtCxdF0YTLCUMlqofHx+PMWPG4LfffsOMGTPg4+ODo0ePwmw2A7AWELKU/EOHDuGbb76Bl5cXBgwYgHLlygG4f5nK/GI2m9GiRQv4+vri8OHDMJlMSgmBXq/HiRMnsHLlSgwdOhQzZ85ETEwMFi9eDJ7nFeGj4ZoIH3744YeOboRG4cHzPM6dO4dx48YhNTUVkZGRGDRoEIKDg/H7778jNjYWCQkJ8PLyQtmyZZGVlYX//Oc/OHv2LPr27Ytx48ZBp9MpWg+rCcov1k3iOZQrVw5ly5ZFXFwc6tWrhzp16kAQBJw4cQILFy5E9+7dERYWhubNm6NcuXJYunQpMjMz0aZNG3h6ehbBE9IoDrQ1b10ctbnAcRxOnz6NkSNHgud5LFy4EG3btlVmfkmScOLECWzcuBF//fUXmjZtCkmSsGXLFoiiiB07duCFF15QzsW6RkEEC9N2eJ6HKIoYOXIkqlSpgvDwcJw8eRKLFy9Gs2bNMHXqVHh4eCjt++STT7Bq1SqMHDkSY8aMQZkyZSCKop35puH8aBqLC0O25Q/YwD9y5AgmTJgADw8PLFmyBK1atbL7O8/z8PHxQbdu3dCpUyd4enrixIkTOHv2LPr164dhw4YpWgpgFSgFXaBJ/Vme51G9enXs2LED165dw969e9GjRw+MGjUK7u7udpXSQUFB0Ol0WLp0KWRZRrNmzZSqaEEQtAWjXAWHuY01nhgWZZFlmb788ktq0KAB9ezZky5evGhXvSxJkhLlYWn7rKBw9uzZ1KhRI7vPFDYsQjV37lxyc3Ojjz/+mIiIcnJylJC4mszMTJo/fz7VqlWLPvzwQ7volYZroO0r5GKQaoFqNpPv2bMHc+fORfPmzfHRRx8hICAAFosFOp1OcZbmNiE4jsMff/yB7du3o0+fPvDz81NMl8KG4zhIkoS33noLx48fx9GjR3Hnzh1UqFDhPg2EiFCuXDmMGzcOABAbGwtPT0+MHDkSgiAo98POq+GkOFCoaRQAdVWw2WymtWvXkq+vL7399tuUkJBw3/HqWV79c2ZmJk2YMMEudb+oYMl6sizT4cOHydfXl1auXKncz8M0EYPBoNQWRUREUHZ2NpnNZjIajQ/UdDScB02wuBgWi0VJf1+7di35+/vT4MGDHyhUHsWPP/5IDRo0oCVLlhS5iaFeAyYtLY0GDBhAL774It2+fZuIHp1tm5aWRvPmzaM6depQdHS0suQDK0PQcE40560LkpOTg5iYGMyZMwchISH45JNP4OXlBSBv5oHBYEB0dDTS09MxadIkeHt7F3WTAVhzZ9zc3ODj44P169fDZDKhQ4cOD20z2bZqbdWqFbKzs/Hpp58qi3ezSJKGk+JoyabxeERRVFZey8zMpI8++ohq1qxJ4eHhlJ2dTUSPNinYOZij98CBA1StWjWKiYkhoqKvz8m9el12djaNHz+eAgMD6X//+5/S/gfdA3P8Zmdn08yZM6lWrVq0bNkyJf3fYrFoZpETomksLgBLf09JScG8efMQFxeHCRMmYOLEiShTpgyAx4eG2d8yMjLw0UcfoWzZspg6dSrKly9v5xAtCljb2Jder4eXlxf27t0LnufRunVru/tUt4X9rNfrERQUBEmSsHTpUhARWrZsCY7jIIqitgm9s+FoyaaRN27dukUjR46kevXq0eLFi+1CxnmBaQS7d+8mf39/WrNmjVKIWBQh5kfBVpubP38+PfPMM3Ts2DG7Nj6K9PR0mjFjBgUEBNCyZcuU9muhaOdCEyxOiHrRJCLr6veDBw+mevXqUVxcnFIpzCItjzqP2gxJSkqi9u3bU//+/SkrK0txBBf38pCs3f/73/+oRYsWNGHCBMrJyXmsOcfamZGRQeHh4eTv70+ffvqp8tmHmVMaxY8mWJwQNuBNJhPFx8fTq6++So0aNaKdO3c+NHycG3XyHDvuiy++oCpVqtD+/fsf+/mihCXpmc1mmj9/PtWrV49++eWXPLWJ/T0jI4OmTZtG1atXpxUrVijnzcnJIZPJVLQ3oPFYNB+LE8IKAC9fvoyRI0fixo0biI6ORrdu3eyKAh/nUyDVroU3btxAeHg42rRpgxEjRsDNzc2hPgmyRXwCAgLw448/4tKlS+jUqdNjoz2sze7u7mjRogVMJhNWrVoFnufRokULCIKgbKim4Ti0p+8kkKoWVKfT4fz58xg5ciRSUlKwfPlyvPTSS/cdlxfYQFy/fj1u3ryJCRMmKA5fRyHLspKNW6NGDfTr1w+HDx/GiRMnAORtuQZRFFGxYkWEh4ejb9++iIiIwNq1awFA2yvaGXCkuqRhRZZlMhqNig/h2LFj1Lp1a3r++efp9OnTdotU58d8YWHYS5cuUVBQEI0ZM4ZMJpPDTYXc95KUlERdu3al7t27U0ZGBpnN5sf6fpjfiMi6+v+0adMoICCAVq9erWxDwkLsGsWPprE4AWSr0eF5HgcPHsR7772HypUrY+XKlQgMDFTMn/xUG5NtxjebzVi+fDmMRiPee+896PV6pebGUajvhYhQpUoVjBgxAidPnsTOnTuh1+vt7uFh52DmTqVKlRTNZf78+VizZo3d3tSOvNfSiiZYnAA2QL788ktMmzYNTz/9NKKiotCkSROYTKYCnZPjOOh0Opw6dQoHDhzA66+/joCAAKdc7lGSJHTu3BkvvPCCYrLld4kELy8vTJ06Fd26dUN0dDTWrVsHi8XyREs/aBQcTbA4CLKtpUJEEEURu3btwqRJk9CwYUMsWbIEDRo0gCRJ4Hk+zzMuESlr3hIRMjIysHHjRlSpUgUDBgyAm5sbAOeqCmYaRbly5RAeHo6///4b69evz7fzVRRFeHl5Yd68eejevTtmzZqFjRs32l2DPReNYqDYjS8NIiKlmI6IaO3atfT000/T//3f/1FiYmKBz8n8DqxA78CBA1SnTh1atWqVU+d2sPViTCYTDRs2jIKDg5WNzvIDu8c7d+7QiBEjqE6dOvTFF18ooXct/b/40MLNDoLneZhMJqxcuRLz5s1D7969MW/ePHh7eyvh5vzCZmS9Xo/09HQsWrQIRITx48ejUqVKRXAXhQOLEul0OlStWhW7du2CLMto3759vrQrdqynpyfatWuH27dvIyYmBmXKlEHTpk2h01mXH9JC0cWAoyVbacVgMND8+fOpRo0aNHPmTMrKylI2bS9oJINFQURRpK+++oqefvppWrFihdPv08PWlmGp/nPnzqXAwEA6efJkgc8niiKlp6fTiBEjyNfXlzZt2qRt41qMaBpLMcJm5rS0NERERGDdunUYNmwYJkyYgPLlyyuRoYLOqCzKkpGRgZkzZ6J69eoIDw+3K1R0NijXCnc6nQ4VKlTA3r17YbFY0LZtW7soVl7ugT0HDw8PBAUFISkpCWvXrkXFihXRrFkzALDbWsQZn4vL41i5Vnpg/o/U1FQaPnw41alThxYvXkwGg6HQci3Y+rabN2+m2rVr09atW4mIir0W6ElghZHz588nf39/Onz4sF15QkFITk6mIUOGUMOGDWnjxo1KnZXFYnGpZ+NKaIKlGGHbnQYEBNDKlSuVpLjCcihKkkQJCQkUHBxMYWFhlJGRYbcOiyvAChQvXbpErVq1ovfee48yMzPtEuLyA/vczZs36d1336VGjRrR5s2byWAwaAt0FyGaYClE1JXE7GcmNOLj46lv377k7+9P27dvV37PtIwnuaZ6uYH//ve/VL16dTpy5Ijd+V1lALH2SpJEUVFR5OfnR4cPH35sJffDUL+Du3fv0nvvvUe+vr60ceNG5XpMc9GydAsPTbAUAWoBI4oi/f333/Tmm29Sw4YNaffu3YXagZnGI8syXb58mZ577jkaMWIEGQyGQruGo8jIyKCXXnqJXnnlFUpNTS0Us4VpLo0bN6YNGzYoDnNHLB9RktEESyHyoOjLn3/+SR06dKCWLVvSkSNHlHyNwjR/2Kw7ceJECggIoISEBJfSUh7Fxo0bqWrVqrR3795COZ8kSZSTk0NDhgwhPz8/2r59u6IlaRpL4aEF9AsBUmVzqlPmT5w4gfHjx8NgMOC///0vgoOD79u9sDAQBAHnzp3Dt99+i/79+6Ny5cpKBMqVkWUZXbp0QYsWLbBs2TJkZGQAyH+FtxqO4+Du7o45c+bg+eefx4cffoh9+/Yp9Vqk1RYVCppgeUJkWYYkSZAkyS6x7fvvv8f48ePh7u6OmJgYtGvXDm5ubhAEAR4eHoWSpMUGgcFgwLp16+Dp6YmQkBC4u7srf3dliAiVKlXC1KlTcfHiRcTFxQGA8qyfBF9fX0RFRaFVq1YIDw/Hrl27lGuqyyI0CoYmWAoR1im/+eYbTJkyBe7u7oiKikJgYKAyENSVyk8K2+/4+PHj2L9/PwYOHIiGDRuWmAHB8lHatm2Ldu3aYdOmTYiPj89X/dSDzsmEetWqVTF37lw0btwYc+bMwd69e5VJQtNcngxNsDwhrAOyr23btmHcuHF45plnsHr1ajRs2LBIK4ozMjIQFxeHGjVqoFevXiUqbZ3jOEULHD16NBITExETE/NE58z9vqpVq4bFixcjODgYkydPxt69e5Wta13dlHQoxeXMKUmoHaPqRKvPP/+c6tWrR0OGDKEbN24oxz5pSDn3tdVOxr1795KPjw+tXLnyvsWzXR0WKhZFkQwGA02YMIGaNGlC586dU/6e3/vN/RlWCJqYmEgDBw6kZ555hr766isisn+3mmM3f7j+tOYAmP3N9sGxWCxYsWIFFixYgK5du+Ljjz9GzZo1ldm2MNdgJVX5f2pqKuLi4tC0aVP07NnTbgGlkqKx6HQ6xS8VGhoKnU6HHTt2KGutMLMlr9pF7mfElpKoUaMGFi1ahGeeeQYzZszAgQMHAFg1P017KQCOlWuuiTqpymg0UnR0NFWrVo2mT59OmZmZytKKRTHLsUxaSZLoq6++In9/f/r888+JyHGr7hcn0dHR1KhRI/r111+J6P5lLp+U27dvU9++fal+/fr0zTffKOUEmsaSP1x/WnMAZFthPiMjA/Pnz8eKFSswZswYTJ06FZ6enkW6mDPZHIq3b9/GokWLEBwcjP79+9sV1ZVUiAhdu3ZF2bJlsW3bNhiNxieO3qg/K0kSKlSogKioKAQHB2PWrFk4cOCA4nBnxz7J9UoNDhRqLoN6Iyz2PSMjg6ZOnUq+vr4UERFBRqPR7u9FlaDGZs5Vq1ZRlSpVaN++fUREpaKgjvk6Pv74Y2rYsCEdOnToiQsU1Z9jyzcQ3SvBaNq0qeJzUfvLSoN2+CRogiUPsM7LitYSEhJo7Nix5O/vT8uXL6fs7GwSRbFYVr+XZZn+/fdfat26NQ0ePJgyMjKUTN6S3tmZ4Pz333+pY8eONHjwYEpJSSm0IsvcE8KVK1fo9ddfp5YtW9KPP/7osC1pXRFNsOQBWZYVn8mdO3dowIAB5OvrS9u3b1e2OzWbzWQwGIplcM+ZM4f8/PzozJkzSq2QK1UwFxT10pLLly+np59+mr799ttCr/NR+2zi4+PpjTfeoObNm9N3332ntKOkP+snRRMsD0FdNcxmqCtXrlBoaCg1adKEduzYYVehXJQOPnW4+tKlSxQYGEhjx45V9s9hbSzpnZ1pjpIkUXJyMnXr1o26du2qFCg+qQmqdgSzaxERXb58mV555RVq3bq1Uu/FhItmFj0YTbA8BLZ3MjNv/vzzT+ratSv5+fnRDz/8oGgKxeHXYIPJbDbTiBEjqHHjxnTp0qUS71N5HHv27KGaNWvSunXriOien6kwc4bYuW7evEm9evWi+vXr04EDB+yEXGl/Dw9Ciwo9BJYur9frcfLkSUyaNAlpaWlYu3YtOnToUOAFr/ML2fJWeJ7HyZMn8f333yM0NBS+vr6lPjrRvn17tGrVChs3bkRKSkqRbcQmSRKqVq2KqKgoNGzYEDNmzMBPP/30RKUFJR1NsDwCQRBw9OhRjBkzBmazGUuWLMHzzz9frPvUsCSxrKwsbNq0CVWqVEG/fv3g7u6uJIeVVry8vDBjxgz8888/yr7N7L08Key5qhPqAgICEBUVBT8/P7z//vv44YcfHL6rpNPiIE3J6VCnjzPV9rvvvqPg4GDq1KmTsmI882UUd+r8V199RX5+frRq1SrFri8NfpWHoTZFhw8fTs2bN6crV64Uevp97nA0EdHff/9NXbt2pVatWtGxY8eIiJS+U5rfiRpNY7FBquQnjuOwY8cOjB07Ft7e3oiJiUFgYOB9K7sXV+p8amoqtm7dCl9fX/To0aNQK6RdGfbsBw0aBJPJhA0bNgCAXTLbk6LeA5qd18/PD8uWLYOPjw9Gjx6No0ePKgWTWvq/FU2w2GBCQpIkbNiwAR988AFatmyJpUuXwt/fH6IoFpqanV+OHj2Ko0ePIiwsDDVr1gRwbyP50tqJ2X3Lsoxnn30WYWFh2LlzJ06cOFEkz4VUyyjIsox69ephwYIFKFOmDKZMmYJjx44p+00XllBzZUqtYCGVn4QhyzLi4uKU1cUiIyNRt25diKIInU6n7PlT1INZ3a6UlBTExsaiadOm6Nu3r9JOjXu4u7srS0bs3bsXBoPBbmmEwkCtnbLix3r16mHlypWoUKECpk+fjt9//91O4BXm9V2O4ra9nAkWTpZlmQwGAy1cuJCqVq1KEydOpOTkZCJyTDKUeq/huLg4evrppykuLo6IXGuPoOJElmX65JNPyM/Pjw4dOqRkyRbFu8vtX/vnn3+oc+fO1KRJE/rll1+IiJRM7NK6V3Sp1lgEQYBOp0N2djYWLVqElStXYtiwYXj//fdRsWJFiKJYpAWFD4NpJElJSYiOjkabNm3Qq1cviKJY7G1xJfr27Qtvb2+sX78eOTk5xRKxkWUZderUwaJFi1CrVi1MmzYNv/76q7JcRmmlVAoWsqmoPM8jLS0NkZGRiImJwYgRIzBr1ixUrFgRgGNXYeN5Htu2bcONGzcwcuRIlC1btvSq1XlAlmX4+/sjLCwMP/30E06cOAEARWKO5DaFiQhNmzbFkiVLoNPpMH36dBw/flzxuZRKHKcsFT8spKyu+xk/fjz5+vrSsmXLKDs7m4jIKUKGV69epTZt2tDo0aOVGiRHt8mZYWHmO3fuUI8ePahfv36UkpJSpKbsg9IOTp48SR07dqT27dvTqVOnlD6nrpAvDZQqwaK2u69fv06DBg2ievXq0ebNm8loNBLRg/cGKm4sFgtNnTqVmjZtSlevXnVoW1wFNmEQEW3evJmqVatG27dvJ6Ki90vlzin6448/qHPnzvTcc88pC1IV5vKkrkCpM4V0Oh3+/vtvhIeH49ixY/jPf/6D1157DTqdzi7b0pGcP38ee/bsQZ8+ffD00087tC2uANlyTFi6QJcuXRAcHIyVK1ciIyOjyN8nCzGLoghRFNGsWTNEREQAAMLDw3H69OlSF4Yu0YKFcu0Rw3Ecrly5gvfffx8nT55EbGws3njjDbu1Ux318tm1JUnC559/Djc3N4SGhmqh5XzAnuFTTz2FCRMm4MqVK1i/fr0yqIvq/QpTHlEAACAASURBVLIN6NjaxpIkoWnTptiwYQNkWcbo0aPx559/Kqv/s35ZkgVNiRYsTGCwjNnz589j9OjRuHz5MlasWIEXXngBgLUmyM3NTclTcQSscx4+fBgHDx7EyJEjERAQUOpmuoLABrVOp1O2P2nXrh06duyITZs24caNG0pmbFE8S0EQFKGiXjw9ICAAy5Ytg16vx4QJE/DHH38ogkeWZVgslkJvi7NQogUL2SI/er0ex44dw4QJE2AwGBAdHY0OHTo4unl26HQ6pKWlYfPmzahWrRq6dOkCvV6vCZUCotPpMHz4cCQlJWHt2rWK5lecZq4oimjSpAmioqIgyzJmzJiBU6dOKcKvJIejS7RgYXb3999/j3HjxoGIsHTpUmXZA0cPWnZ9pqIfPnwY3377LQYNGgR/f3+HDIaSADM1AgMD0adPH2zevBmXLl0qlvCv2uRiGnOLFi0QFRWFtLQ0TJs2DWfOnFEyuYvSRHMkJU6wMD+FKIqQJAn79u3DhAkTULVqVSxduhTNmzdXkuMcOWBZ5xdFERzHIT09HV988QUaNGiAl19+GcC9QkeNguHm5oaQkBAIgoCtW7fCaDQW+TXZO2PmEDNlg4ODsWTJEoiiiIkTJ+LChQuKecZMo5IkXEqkYGFs3boV48ePR2BgIKKjo9GoUSMAzjNgWWcSRRE//PADzp49i7CwMFSrVg2AfX2KRt5Rv9vAwEC8/fbb2LZtG3799ddiu766+p1tehYUFISIiAhkZmZizJgxOHXqlJ1juSRR4notz/OwWCzYuHEjZs6cifbt22P+/Pnw9/eH2Wx2dPMU1FpTUlISlixZgqCgILz++uslrpMVN8y3JkkS9Ho9evToAQ8PD+zYsQM5OTnF3hb2XZIkBAUF4dNPP0VWVhbCw8Nx5cqVEulrKRGCRa1GmkwmfP7555g6dSp69uyJyMhI1KpVC6IoOt3sL8syBEHAnj178Ndff2HIkCHw9PTUBMsTwrQA9r4bNGiA/v37Y9euXfjzzz/tqseL+lkzPwozi0RRRPPmzbFy5UrcuXMHw4cPx+XLl6HT6ezWfnH5PlCIyXYOgW29IcsyZWZmUmRkJNWpU4emT59OKSkpjm7eQ2Ep6PHx8dSyZUtlj6DSsPFYcSPLMl27do06depEAwcOpNTUVKV6vLizrNlKcxaLhQ4dOkStW7emnj170oULF4jo3va9rr53kXNN4QWAbNudpqamIioqClFRUXjnnXcwffp0eHl5ObXk53kea9euRXp6OsaMGQNPT09HN6lEwiqQQ0ND8fPPP+PYsWMAin+rVLa6HNOW2rdvj8jISNy4cQOTJk3CxYsXncb/98Q4WLAVGLVET01NpXHjxpGvry9FRkZSdna2sl2Go+t+HgRr0/nz56lx48Y0bdo0pdZF206i8GFr0aamplKPHj2oa9eudPfuXYeslcJ21GSaqSzLdOjQIQoKCqKXX36ZLl++bLenkavikoJFkiSlaDAhIYGGDh1KPj4+FBsbSzk5OUTkHMWEuVFvcGUymWjUqFHUrFkzunLlChFRqap+LU7UfWH//v1Us2ZNWr16NREV/8JZuSuiWeHkkSNHqHXr1vTSSy/RhQsX7EwmV5xoXFKwsBdz/fp1euutt8jf35+2bNlS6FttFiaszWyWPHLkCAUEBNAnn3zitG0uiWRlZdGbb75JnTp1otu3bzu0Lcw/yHw9P//8MzVo0IB69eql7Djgqvtyu6SPheM4XL58GZMnT8bRo0cRFRWFvn37KiE9Z0WWZeh0OuTk5GDbtm146qmn0KtXL0c3q8RDKl9K2bJlMXnyZPzzzz9Ys2aNA1tlhUWuiAjPPfccVq9ejatXr2LkyJH4999/lfR/l8PBgi3PqH0PFy5coC5dulBgYCB98803ijR3hgWaHgWzm3fv3k0BAQG0du3aYt2bqLSSu0+YzWYaO3YstWjRgi5dukREjuk7ubdpZdv6/vDDD9SsWTN65ZVXlPaxKKKrrOviEhoLqbYZPXbsGMaNG4fMzExER0eja9euihfd0Wn6j4JstSNpaWnYsmULateujRdffFGpJ9EoOtR9gmyJiSEhIcjJycGmTZtgsViU1Pribpe6KppFhFi0KDExEe+//z4uX76sZO+6Suq/SwgW9gKYUDEajVixYgU6duwIk8nk6OblGbIVGv78888ICwtD7dq1i20PaA0rbJJq2bIlBg0ahB07duD06dPQ6/UOfQ9s4mHfX3zxRUREROD8+fOYNGkS/vnnHyWJThMshQhbo8Tb2xsrVqxA8+bNlfUsXOFBs0LDVatWITg4GH379i2RxWfODtNe3NzclL2Idu7cCaPR6HBtl2wZuqw/dOzYEYsXL0ZCQgLGjx+Pmzdv2q0Z5NT9xhH2V15gNqfZbKatW7dSo0aNaMCAAUqGojp066wwu9hisZDFYqFNmzaRv78/7d69W/m7M7e/pMKeudlspsjISKpXrx59++23dn93xLvJHYpmEcT9+/dT/fr1acCAAXTt2jU7X4uz+hWdVrDIskxGo5E2btxI9erVo9DQULp27Vqhb/pdlLDOYbFY6MaNG9S6dWsKDQ0lk8nkMvdQ0rl69So9//zz9Pbbb1N6ejoR2TtVHQVLTWAJdQcPHqQGDRpQSEgI3bx5027HCWcULE5rCsmyjK1bt2LKlCno1asXli1bhtq1aytr07oKZCs52LJlCxISEjBmzBhlGUwNx1O3bl2EhITg0KFDOHfunPJ7R++LTbkWgHrxxRexYsUKnDhxAu+88w6uX79uV7jodDhUrJH9dpVqFXXJkiVUs2ZNmjRpEiUmJiq/Z3sCuQLsnv755x969tlnadSoUZSVleW06mtpg/W7hIQE6tmzJ7322mt09+5dp0ipZyFo9sU036+++oqaNGlCb775prI1DNPincm0dqhgYS9WnaOSlpZGCxcuJD8/P5o8eTKlpqY6ZXp+XmCZldOmTaPAwEA6f/68ot664v2UNNSZ0Fu2bCEfHx9lLyJHCxY16gxdi8VCe/fupfr161NISAhdv35dKRFxpjozhwoWtTQmIkpOTqYZM2ZQrVq1aMGCBWQwGBxW3l5YHDt2jPz9/WnOnDl2M4+zdIDSDpvl09LSqGfPntSxY0dKTk52qj7H+g0rWRFFkfbt20dNmjShQYMG0a1bt5RJ2lkEosMES+6tKVNSUmjcuHHk7+9Pq1atoqysLDtJ7QoDkXVE9t1oNNLw4cOpRYsWdPHiRTtB6gr3UxpQVxsfOnSIfH19acmSJUR0//t0JOrMWzbZbtu2jRo2bEghISGUmJhoN0kTObbdxS5Ycj8gImuF8v/93/9RgwYNaM2aNWQymZTjXckMUnvqiYi+/fZbatCgAX366ad2gsRV7qc0oA7xms1mevvtt+m5556ja9euKb9zdIRIjVozMZvNtG3bNvLz86MhQ4ZQfHy8nXbjSK2rWEMTpFr/E7AmK8XHx2Pq1Kn46aefMHv2bISFhUGv1yvp1a648I0gCEhPT8fOnTtRpUoVdOnSxS4K5Gr3U5JRL3yt1+sxbtw4xMfHY+3atcomcs5UcsHayjK2e/fujWXLluGnn37C+PHjkZKSYreAt8MobklmsVgUjeTChQv0yiuvUNOmTenLL78konubZztiEZ4nRZ3/sG3bNqpVqxatXbuWiMgl76c0YjAYKDw8nBo3bkx//PEHEZHTma7qxEumuezZs4caNmxIgwcPpuvXrxORYx3QxaKxqFPXOY6Dm5sbfvvtN4wZMwa3b99GZGQkunbtCkmSlJndFVcuZzVNWVlZ2LRpE5o0aYKuXbu6VN5NaUaWZbi5uaFv377Q6XTYvn07LBaLXZq9M8C2FWFFtzzPo2fPnoiIiMCxY8cwZ84c3L59265wkY3B4qLIBQvZ1khR3+Dx48cxatQo5OTkKBXK7CGxB+WK5gLZCtwOHTqEM2fOICwsDDVq1LBbMV7DuSEiBAYGYtCgQdizZw+OHTvmdH1Rbb6pCxcbNWqEBg0aYN++ffjwww+RnJwMnuchiiIsFkuxCsdiESysNFwQBHz55ZcICwvD3bt3ER0djeeffx4Wi6VEbM7FcRxu3bql3FefPn0UYeNMM57Gg2H9z83NDX369IGHhwe2bt2KnJwcp+2bzN+SkpKCpUuXonXr1li9ejXOnTuHyZMnIykpSRl7xUmRPC1SpSMzaWqxWLBp0ybExsbi9ddfR/v27fHFF1/g9OnT96014WqDUN3mPXv24OLFixg0aBDKly+vrMzuavdUGmGTgCzLqFu3LgYMGICvv/4ax48ft9ux0JneJZu4t2/fjoSEBLz77rt4+eWXsWDBAiQkJGD27NlITEy0O75Y7qEoHDfqkJcoimQymWjjxo3UqlUr+uyzz8hkMlFCQgLNnz+fevXqRd999x0ZjUbFseushVUPgoWYJUmia9euUcuWLemtt95SkvvUx2k4P+r3lJCQQJ07d6awsDBKT0+3S513JpKSkujVV1+lI0eOEBEp4+ezzz6j2rVr08CBA+n69et2Tt+ivodC11hIJQ05joPRaMT69esxf/58jB8/Hu+88w7c3NxQtWpVjBkzBu+88w7mzZuHffv22e25Qk40KzwKUs0AsbGxyM7OxsSJE+Hu7q6FmF0Q9Xvy8fFBWFgYfv31V/z22292wQVn6p9xcXHw8fFBq1atYLFYoNfrcfLkScTFxeGTTz6Bh4cHRowYgevXryu+zCJ35BaFtGIzdXx8PE2ePJl8fHxowIABlJycrPydSU2LxUL79++nPn360ObNm11qXU+ie9tHnD9/npo2bUrTp08ng8GgrK6u4bpIkkTJycnUu3dv6tq1KyUlJTldrVdOTg516NCBdu/ebbd/0ujRoyk6OpoMBgPdunWLxo8fTwMGDKDTp08TUdGHogtFYyGbbSqKIkRRhCAISEhIQHR0NG7fvo1Ro0bBYrFgyZIluHDhguJMYv6HHj16IDQ0FHFxcThy5MgTt6c4fTUcxyEnJwefffYZAGDo0KFwd3eHIAguGTLXuAcRoXLlyhg2bBjOnj2Lb775BoIgKH7DorgeqZz9pPL5PIzLly9Dr9ejZcuWyrj6+uuvkZqaqjigq1atitmzZ6Nq1apYsGABTp48qfiMimod3UITLJIkKYsSnz9/Hh988AFEUURERARmzJiBiIgImM1m/Oc//8HPP/+sfJapZW+88Qa6d++OmJgY3Lp1q8AvjrVFFMViidtzHIcTJ05gz549eOutt+Dv76/ks2jmj2vDQrXt2rVD+/btERMTg7S0tCJzxqvzTVj/fdAkyQQCAPz2228ICgqCt7c3OI6DyWTCr7/+imbNmsHX1xeAtY8+9dRTmDt3LurXr49Zs2bhl19+AWDNMSuKHJdCESwsnu7p6YkbN25g3rx5qFSpEqZPn44qVapAkiT4+flhxowZaNOmDRYuXIjz588re6awGSAkJAQVKlTAzp07lfVsCwIRKYsjF7XWkp2djY0bN6J69ero3bt3kV5Lo3hhg61cuXKYOHEibt26hdjY2CKdNNh59Xq98nPuvC51n7569SqCgoKg1+sBAImJiTAajWjZsuV9GrOXlxcmTZqEDh06YNasWfjpp5+U6xT2/RRYsFCusBXP8zh58iQ++OADBAYGIjw8HNWrV1ckriRJKFeuHN5991106dIF8+fPx7Vr1xRnmCRJ8PLywtChQ7Fr1y5lNa/8mjRsi419+/bh2rVrRaayMg4ePIgff/wRw4cPR926dQv9WhqOg/UdSZLQokULvPLKK1i/fj0uXLgAIP9981GozSuDwYD9+/fj8uXLisvgQcdbLBakpaWhcuXKyiR969YtlCtXDn5+fvd9RpZlVKxYEaNGjUK/fv0QERGBffv23ZceUhj3VGDBIkkSzGazktV37tw5zJ49G4GBgRg/fjyeeuopAIBOp4NOp1OkvLu7O4YNGwY3Nzfs2bMHoijaFSe2bNkSvr6+OHTokF3Wbn5uNiEhAdOnT8fx48cLenuPvXdZlnH37l1s2bIFderUQZcuXbR8lRIGz/PQ6XTQ6/Vwc3PDW2+9hdTUVGzevNmubxZGkSLTGgRBgMFgwKRJk/Ddd989MHGUHSfLMiwWi+L3AYCsrCyUKVMG3t7eD7wfwKqBjRw5Eq+++irmzJmDAwcOKPfB3BlPSoEFi1oTOHLkCKZNm4bevXtj/Pjx8PDweOjnZFmGh4cHpkyZgh9++AHx8fEA7KX/sGHDcPz4cRgMBrvQdV6RZRnZ2dlPZE49CtYJDh8+jF9++QUhISGoWbNmkTn1NBwL8wPWr18fo0ePxs6dO3H06FHodLoiKT8hImRlZcFsNj+2Xex4htq98KgJWRAEDBo0CNOnT0dkZCTWr18PURQLbXIssGDheR56vR5ff/01IiMj8dprr+Htt99+rF+DScb69eujUqVKOHz4sN1GTJIkoUmTJhBFETdv3ixwZKWol1tIT09HTEwMgoKC0KdPn2Iv8tIofsqUKYNXXnkFnp6e2L17N4xGI4CiyWl5lMBiY0UQBLi7u9tNoJ6enjAajUhPT3/kOYgIbm5u6NGjB0aMGIENGzZg9erVkGW5UKKZeRYsatUPAERRxLZt2xAbG4uhQ4diyJAhilB51BdTx3Q6HYKDg/Hjjz/e92LKlSuHWrVq4dChQ3aFVvlpK4AnGui5w3257c9vv/0Wf/31FwYOHIjKlSsr96RRMuF5HpIkoUGDBggJCcGBAwdw9OhROzM+L18A7utPrJ/lXgWAkft4dqwgCPDy8sLdu3eVvv7UU0/BaDTixo0b97XrQREmd3d3vPnmmxg7dix2796N1atXIycnBwCU6GpBBGe+BAsLg1ksFmzYsAFbt27F6NGj0a9fP8WXovanPOhLXe5dt25dGAwGxWYUBEFRL+vUqYNTp04VqNrZ3d1dWZ6hoKjbq95Xl+M4JCYmIioqCi+++CJ69uwJAEqhpUbJhci6lUv//v1RpUoVrFu3DiaT6ZH9PfcXgPv6E+tnrO+zv6uXEHnQsQDQoEEDnD17VvHzVKtWDaIo4q+//gKA+z6n/jfrsxzH4dVXX8W8efOwZ88eLFq0CNnZ2RBFscCaeJ6nWPZQcnJy8MUXXyA2Nhbt27dHVlYWtm3bBk9PT+Vmc5sh7GcmeNjNnD9/HmlpaTh16hR4nofFYoHZbAbP80hKSsKvv/6KxYsXK+pZXiQnz/OIj49HZmYmDhw4gLt370IUxXw9FMBa4arX6++7LtuY/o8//oDRaERISEiBzq/hWjCtmRXMXr16FWfPnsXu3bvh5+eXZwcuExZqxzBgv3dzcnIyZFnGzZs3cenSJRgMhvvME/UkfeLECVy9ehVVq1YFAFSuXBlxcXGIj49/6KSs0+ng7u6u/JsJr0qVKuHTTz9FdnY2pk6divLlyxfIpcBRHvUcIoIoirhw4QImTZqE06dPo0KFCtDr9coDV8/aD/qZ4zi7zbeNRiNMJhMqVqxopxHxPI+cnBy7RXbyGhnieR4mkwkJCQnw9vaGl5dXgbz2jzK/LBaLIs1NJlOxRoKYSeps0SfWLmfgQclkT/q81NoGcK9PV65cWRkDuY99VLvYv9XBCSYsJElCQkICvLy8ULFixQdmx7LjRVFEWloaatSoAZ7n4eHhgfT0dCQmJt7XDvX1ck+YakEliiI8PDwwePBgvP/++6hQoUK+tfE8CxaWfm8ymXDjxg0kJiYqpgtwz5nLPOhubm7Q6XSKk8nNzU1RJdUJRurBqZau6pAaeyh5gRVgjR07FuPGjUNoaCgMBkO+Hoq6XawtuQsKHVWMps7KVD8rRyPLsl0Uw5GCL7dgKcosbDbg1f3jYdfKPVmZzeYHPqfU1FSEh4ejW7dueOONNxQt/kHnYu9e7ZtR980HHcN4kADmOA5ly5aFIAjQ6/Vo3LgxvLy88vtY8m4KMRVQp9PBz88P9erVs2uUOvSlVuvUZtGDwrFq51dh+SiSkpKg1+tRpUoVVKtWrUDnyH1PzjB4GQUJwZcmcg9WZ3pOTOgwTfxB4+b27dsAgIYNG6JTp05F2v/UfUk9FhmSLCmO4vyQZ8GiVqOs0k2yCZvcElDdQCjHqY/JHZJ+0A0VlAfN4gU5L5Pg1nMBknT/OTjb/2y3bftgvi+VL5hWl9u77ww4ywB+0HMpyrap+wrw8FCx3YC17QCQ+xxMS1cXH7IV+R927Qf97nHabO5jclsGPM+DZBk8+HvXVvfzx5Cv+Chvu2me4yDLVh8DSACBA3EyeI7AgQPHWa9PPA8enPXnR2gkRZGx+qQDTx3m5jmAEziwp6o+K0cAcYCFt/5VIIAn2zsogr6cW1txlsEMOM8aJbn7WVG0yzYMwZEMEIHnCOB4EO5pIAz1O3qUCa3us+rJN7dJo+ZBv8s9kT+I3Odn5+I4DgQCkWy9PxAgEWRwkGQZEKxjmkgGz9v8NJxNUPEcBM6WTvLAqz4AjuMAsjUIBOIkcGQdVbLMg9NzEGXr7wReAHje9ohtgibXA3jcv5+E3BL/Sc5tvW/ZKhzt/2L9RgA4Atl+5Dn7Q7i8ivj8tMdJcda2FXa7CDbBQgQBkjKB0GOm9AdFStX/VvtI1BpQ7nB1fnjUZx7VHuIIHHHWMS4DnE4AD7U5ZBOQ4GA2m8EJAkiWIQj5FCzWqxM4SABJgCyDEwTwgs4mwQCO04Egg+M5gJOtUzlHAByzLklhdSjKJVas/yKACKSS0Ey4SJxVa+HyoTpquBYcWd+2+vVa53c2nRbgnDaTJLdZUvyaINnsewC8Dod++B6LFi1CSkYG3D09wEEPUbTAZMpBn959MXLUcLh7eoBXjbd8popKAEzgOOuFr/4dj+9++AF/X7mCmtVroku37gioVw+cTgAggeNEcOCRL+OsEPD29kZYWBgCAgIK8axWccLZBAxHtu1MOA4EAYII8AIPieMgg8CT6mMaJQqrUUzgbAYRU1lEiUCcDB3HF+i1MwHi5uaGQYMGoVmzZgAend5fJJD1/pgTsWrVqmj/Qjtk52Rj157duPRXAgaEhqB2repo3PQZ6N3cwIODoFLX85fHYrFAp8uBxZyD1bHbEBW9Epw7UL6cO8QsIzJzzBgwcBAmTZsCr/JlIUtm8CDoBXcU5wgjIqXqszDqHoj5TCBbHzhJSEpMxCcff4xrt5JA4FGG06FXr15o16MrnqpcGe4E6MABPK8JlxKG1echASQCsoyMzEx8/c132LvvG4AT0O2lTujTuxcqVKgAIO+b76mjqSyHyzFlIjIIEqzmjgBZkgDZAl5HGDRwEA4e/gNbd+7A80HNIMNqj3CQbP5V673mI77LgRd4cDzhl6NH8PH8hfD3a4jNW3fg2G+/YOeuLajn74uYmM/w/Q8/Qg8ORAJ4TofiHlksnb9IloYkgGQZKcm3sTluE/488wc4gUPq7TsYNXw45n00F5nG7KLx3Go4BVa3mwhZkmAyGvHJggWYNGkK7qakIj0zA3u//BLXrl3LdwBB7ZBneWCOgmnmZG2QzU8qgScZ4HirD5W7Z/pZv6ky1PN8JQJ4jofZaMLPh35GZloOQkMHolmTxjCZzfD3q4V3h72DlDu3cfz4CYgAOJ7P1yVcA7J2LJIBSUanrl2xPi4OWzZvQ3CLIHz37be4deeOLRnJ0W3VKCp4zqr6p6Sl4Kuv9sO/Xj3EbdmMHbt3YumyZfD39wfg+vOLNTYEm+CwaewQFH8igyPOTn/I+6i3DSZjjgGXL/0DvUd5VKxsXUzGXacDOB7VqtcAwOF2cjrMADhZBi+LcPURRpwMkM0ZTVZfC08y3AlwhwA9r0emyYBMiwg3Ny+4C2WsD55kzQwqgRBxkGUdZOIg8DIEHY/r//6LLVu2Iy01AzWrV4NH2TKQZYst0GE1me6NUieHOIB4yGQ1imTO5m+ROfAyD5AAgLdFQSVwnGSNIMm8cn95r262zdQgQBJlQNCBuWY5AjhOD0hWTwQHHXjbpTk4R/3Ik8BBtjqswVmnIJ6Djueg43j8eOA7DAwLRehboRB5YNy4iajhXdX2QVfoRRoFghcADqjkXRFD330HxhwDpk+ZjLcGhWFN3BZk5Bis/gZiwWmyhaNdBGIj2DaXAtZ/E8vnIpsTW7YdxT7DjszrdQiQZYJe74Hq1X1gNBqQlZVuPTmnA8Aj+c5t6HgdqlXxhh6wDUKh5M3aHCBzBJkD3GwVov/73wXodTw6d34Bbm42305JswI1rHAAwQJwMnS8B959ZwS2btqKN/r0wOkTRzBh3ER8d/BniCQAvA7ECTZll1SD1NmxRix4snZjjuMBzmYCkWQLZDA4u29APro+x3GAwMGzTHk893xbmMwZOH78F9xNzYBokZGcfBebNm2Ct3dltGnd8l5jXEhI5wciQCJC67ZtsfzTTzFixHu4+L/z2Lp5q6rYS5MsJRMCJ7BEJT3c9WXR4YWOWLl8MeZ9OAXZOdk4+P1hGM0Wq1ABpwgWVxoQVp3Fav4wTYXT66HXc0pGPcf6+L3EdAD5yGORYVu1ihPwfLv26N//VezYvhEXzp1G3do1cPXqXzj523E0aPgMKlWsgJRsI8rpdQDvqPS4woOje93BmmhLkCFDJBkcL6BsubIYPGggvty9F7t3bkPIwFDUrO4NieRc2YoaJQICREkERzISrt/AiaN/oFXr1qjg7QGLxbpubK2aPqqopJKv4CJYhSZHMjgIkIlAMgDIePv/hqJjt9vwq+UDiyiC5wgCb81VI1m2BWzylSBHII6DJAmoVbM2IqMWoP2+r/HjwcNISrqDVs+1RnCL5tixbRcG9A/BrDnz8PbA/nDzsEa5XR373FurvSwTwSxaYBZF+Pk9jeCg5tiw7SscOfoLBrz+KjibD931717DHg486cDzQFZ2OpauiIb75+XBuwE3bsajXdvn0avnS/B004Mj0RYZ4gCZy1Xz4eTYIDdujQAAAd5JREFUMshBVk+KJPNo90IHtON1EEVr+Q7H8VBGB2cLRSMfCXIWkiDKMvQyB16WQHoR4HWApIMkEjhBhmjKwcGvv8eaTTsQ3LY9Rg5/G+U93MALLm4SkAiQNcOWIEOmHKTcvoV1n2/A0880R5eePVCBt+DYkV+w/+DPaNOxMzp0aA83gYOec/F717gPWSbIkgwiE0QxC/+7cBHf/3AMibeT0bBJY3Tu3Bk1q9eAG0fgOGvRrrVYl7eVuzj6Dh4DyQBYFFSwmf0yCLItQop7hhDPQ+CsJTxEMjjeuiJe3hd6gnVtBoF4cCSDeBHEAwLpQeAhk2hTiXikp2chy2BAlcqVoNcVczpykSDb1BUexAGybIa12Nm6pq5ZlqDnJMWJDQAWWYbAW21RjZKHtZxHBAcLON7T/m8AZJLBk2xTUKzhW6Xs3+mx+YKU9Apr2Nlah6yqI4KtOBK2mkCi/GssGhoaGnlF09M1NDQKHU2waGhoFDqaYNHQ0Ch0NMGioaFR6GiCRUNDo9DRBIuGhkahowkWDQ2NQkcTLBoaGoWOJlg0NDQKHU2waGhoFDqaYNHQ0Ch0NMGioaFR6GiCRUNDo9DRBIuGhkahowkWDQ2NQkcTLBoaGoWOJlg0NDQKnf8HovmOUshMbSgAAAAASUVORK5CYII=)
Maths-General
Maths-
Solve ![fraction numerator 4 x over denominator 3 end fraction plus fraction numerator 2 x over denominator 3 end fraction equals x over 3 plus 5](data:image/png;base64,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)
Solve ![fraction numerator 4 x over denominator 3 end fraction plus fraction numerator 2 x over denominator 3 end fraction equals x over 3 plus 5](data:image/png;base64,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)
Maths-General
Maths-
Show the conjecture is false by finding a counterexample. If the product of two numbers is positive, then the two numbers must both be positive.
Show the conjecture is false by finding a counterexample. If the product of two numbers is positive, then the two numbers must both be positive.
Maths-General
Maths-
Use the Law of Detachment to make a valid conclusion in the true situation.
Jim works every alternate day. He worked yesterday.
Use the Law of Detachment to make a valid conclusion in the true situation.
Jim works every alternate day. He worked yesterday.
Maths-General
Maths-
Show the conjecture is false by finding a counterexample. The square root of any positive integer x is always less than x.
Show the conjecture is false by finding a counterexample. The square root of any positive integer x is always less than x.
Maths-General
Maths-
Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅.
If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆.
Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅.
If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆.
Maths-General
Maths-
Aaryan has Rs 50 and saves Rs 5.50 each week. Charan has Rs 18.50 and saves Rs7.75 each week. After how many weeks will Aaryan and Charan have saved the same amount ?
Aaryan has Rs 50 and saves Rs 5.50 each week. Charan has Rs 18.50 and saves Rs7.75 each week. After how many weeks will Aaryan and Charan have saved the same amount ?
Maths-General
Maths-
Explain how you can prove that AB = CD
![](data:image/png;base64,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)
Explain how you can prove that AB = CD
![](data:image/png;base64,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)
Maths-General
Maths-
Show the conjecture is false by finding a counterexample. All prime numbers are odd.
Show the conjecture is false by finding a counterexample. All prime numbers are odd.
Maths-General
Maths-
Solve ![fraction numerator 4 x over denominator 5 end fraction minus straight x equals x over 10 minus 9 over 2](data:image/png;base64,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)
Solve ![fraction numerator 4 x over denominator 5 end fraction minus straight x equals x over 10 minus 9 over 2](data:image/png;base64,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)
Maths-General
Maths-
Complete the conjecture. The sum of the first n odd positive integers is ____.
Complete the conjecture. The sum of the first n odd positive integers is ____.
Maths-General
Maths-
Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If an element is in set A, then it is in set B.
If an element is in set C, then it is in set A.
Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If an element is in set A, then it is in set B.
If an element is in set C, then it is in set A.
Maths-General
Maths-
Explain how you can prove BC = DC
![](data:image/png;base64,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)
Explain how you can prove BC = DC
![](data:image/png;base64,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)
Maths-General
Maths-
Use the distributive property to solve the equation 28- (3x+4)= 2(x+6)+x
Use the distributive property to solve the equation 28- (3x+4)= 2(x+6)+x
Maths-General