Maths-
General
Easy
Question
The conditional p → q is only false when
a. p = T, q = T
b. p = T, q = F
c. p = F, q = F
d. p = F, q = T
The correct answer is: So, p → q is only false when p = T and q = F. Hence option b is correct.
Hint:
p → q is a conditional statement which mean if p then q. The conditional statement is saying that if p is true, then q will immediately follow and thus be true
Solution
The truth table of p → q is given as
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAADCCAYAAABgzEqRAAAHCElEQVR4nO3dMW7U7BqG4e87ygYiUf4FGtgLs4RxlzYpaCmACiiYBSQtnb0ClDSshFhZAFKW4FMcZXT4CSQTPHaeyXVJLiIG8Sp6NffYJHYdhmEoAECM/8w9AACwHfEGgDDiDQBhxBsAwog3AIQRbwAII94AEEa8ASCMeANAGPEGgDDiDQBhDu56Qa11ijkAYO+N9TiRO+M95j8Gd6m12jcmY9+Y0pgnwy6bA0AY8QaAMOINAGHEGwDCiDcAhBFvAAgj3gAQRrwBIIx4A0AY8QaAMOINAGHEGwDCiDcAhBFvAAgj3gA8SN/35e3bt3OP8SSJ94iWy2VZr9dluVyWWmuptZaTk5O5x2KPvXz5crNrN7vXdd3cY/GIjfk+tVgsyvX19Z07Z0/HJ94je/PmTTk6OirDMJTLy8tydnZW1uv13GOxh5bLZSmllGEYyjAM5erqqlxcXMw8FQnGfJ/68OFDOTk5KV+/fr31z+3pboj3yI6Pj8tqtSql/O9T6fHxcfn27dvMU7GPLi4uysePHzdfn56elhcvXsw4ESm2eZ+6OWP+3fHs2bNyfX1dXr9+fevft6e7Id479vz587lHYA/1fV9KKeWff/6ZeRL2wZ/ep27OmH93/PjxoxweHv4U6Bv2dHfEe8eurq7mHoE9tFgs5h6BPfI371Pv378vp6enmzP5/2dPd0e8R3Z2drb5QYy+78vZ2Vk5OjqaeSr20atXr34621kul+Xy8nLGiUgx1vtU3/fl8PDw1nDfsKe7cTD3APvm+Pi4fPnypTRNU0op5fPnz39cbHio8/Pzzf87llJK27bl+/fvM09FgrHepxaLRfn06dMfX2NPd0O8d+D8/HzuEXgihmH46et3797NNAlppnyfsqfjc9kcAMKINwCEqcO/r2f8+wW1/nLJA3bFvjEl+8aUxtw3Z94AEEa8ASCMeANAGPEGgDDiDQBhxBsAwtzrDms3t7WDKdg3pmTfSHSvePs9SKbi926Zkn1jSmN+UHTZHADCiDcAhBFvAAgj3gAQRrwBIIx4A0AY8QaAMOINAGHEGwDCiDcAhBFvAAgj3gAQRrxHsl6vS631t0ff93OPyB6xb0zJvj0+dbjjkTqeurO9rutK0zS+bw9g37Zn3x7Ovm3Pvj3cmPvmzBsAwog3AIQRbwAII94AEEa8ASCMeANAGPEGgDDiDQBh3KSFR8W+MSX7xpTcpAUAnjDxBoAw4g0AYcQbAMKINwCEEW8ACCPeABBGvAEgjHgDQJiD+7yo1rrrOWDDvjEl+0aie8Xb7QOZittVMiX7xpTG/KDosjkAhBFvAAgj3gAQRrwBIIx4A0AY8QaAMOINAGHEGwDCiDcAhBFvAAgj3gAQRrwBIIx4j2S9Xpda62+Pvu/nHpE9dNuudV0391jsKfv2eNThjkfqeOrO9rquK03T+L49gH3bTq21tG1bVqvV3KNEsm/bsW9/Z8x9c+YNAGHEGwDCiDcAhBFvCNc0jR+OZDL27XEQbwjXtm0ZhmFzLBaLuUdij9m3x0G8ASCMeANAGPEGgDBu0sKjYt+Ykn1jSm7SAgBPmHgDQBjxBoAw4g0AYcQbAMKINwCEEW8ACCPeABBGvAEgjHgDQJiD+7yo1rrrOWDDvjEl+0aie8XbvX+ZintNMyX7xpTG/KDosjkAhBFvAAgj3gAQRrwBIIx4A0AY8QaAMOINAGHEGwDCiDcAhBFvAAgj3gAQRrwBIIx4j6zW+svRdd3cY7Fn1uv1rbt2c/R9P/eI7BH79vjU4Y5H6njqznZqraVt27JareYeJZJ9217XdaVpGt+3B7Bv27NvDzfmvjnzBoAw4g0AYcQbAMKI9w40TeOHOQDYGfHegbZtyzAMm2OxWMw9EgB7RLwBIIx4A0AY8QaAMG7SwqNi35iSfWNKbtICAE+YeANAGPEGgDDiDQBhxBsAwog3AIQRbwAII94AEEa8ASDMwX1eVGvd9RywYd+Ykn0j0b3i7faBTMXtKpmSfWNKY35QdNkcAMKINwCEEW8ACCPeABBGvAEgjHgDQBjxBoAw4g0AYcQbAMKINwCEEW8ACCPeABBGvEdWa/3l6Lpu7rHYU/aNKazX61t37ebo+37uEZ+cOtzxSB1P3dlOrbW0bVtWq9Xco0Syb9uxb3/Hvm2v67rSNI3v2wOMuW/OvAEgjHgDQBjxBoAw4r0DTdP4YQ4mY9/g6RHvHWjbtgzDsDkWi8XcI7HH7Bs8PeINAGHEGwDCiDcAhHGTFh4V+8aU7BtTcpMWAHjCxBsAwog3AIQRbwAII94AEEa8ASCMeANAGPEGgDDiDQBhDu7zolrrrueADfvGlOwbie6Mt1sHAsDj4rI5AIQRbwAII94AEEa8ASCMeANAGPEGgDDiDQBhxBsAwog3AIT5L8slWf0+Hxq+AAAAAElFTkSuQmCC)
Hence, we can see that p → q is only false when p is True and q is False.
Final Answer:
So, p → q is only false when p = T and q = F. Hence option b is correct.
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Solve for x: ![fraction numerator 3 over denominator x minus 4 end fraction plus fraction numerator x minus 5 over denominator left parenthesis x minus 4 right parenthesis left parenthesis 2 x plus 3 right parenthesis end fraction equals fraction numerator 4 over denominator left parenthesis 2 x plus 3 right parenthesis end fraction](data:image/png;base64,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)
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Maths-General
Maths-
solve for x ![fraction numerator 3 over denominator x plus 1 end fraction equals fraction numerator 8 over denominator x plus 2 end fraction minus fraction numerator 5 over denominator x plus 3 end fraction](data:image/png;base64,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)
solve for x ![fraction numerator 3 over denominator x plus 1 end fraction equals fraction numerator 8 over denominator x plus 2 end fraction minus fraction numerator 5 over denominator x plus 3 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Verizon Wireless offers an internet plan for $20 a month plus a $20 setup fee. Consolidated Communications offers an internet plan for $25 a month plus a $10 setup fee. After how many months will the plans be equal?
Verizon Wireless offers an internet plan for $20 a month plus a $20 setup fee. Consolidated Communications offers an internet plan for $25 a month plus a $10 setup fee. After how many months will the plans be equal?
Maths-General
Maths-
A boy buys four video games from the store and a Frequent Gamer discount card for $10. Later that day, he goes back and buys two more video games. He also got a $2 discount using his new card. If he spent a total of $218 at the game store, how much did each video game cost assuming every video game cost the same amount?
A boy buys four video games from the store and a Frequent Gamer discount card for $10. Later that day, he goes back and buys two more video games. He also got a $2 discount using his new card. If he spent a total of $218 at the game store, how much did each video game cost assuming every video game cost the same amount?
Maths-General
Maths-
A local baseball team bought 75 shirts from a t-shirt company. The team was charged $6.25 for total shipping but received a $20 team discount. If the total bill was $398.75, how much was each t-shirt?
A local baseball team bought 75 shirts from a t-shirt company. The team was charged $6.25 for total shipping but received a $20 team discount. If the total bill was $398.75, how much was each t-shirt?
Maths-General
Maths-
Soda is on sale for $0.20 off each 12-pack. A man bought 4 12-packs and paid a total of $4.20. How much did each 12-pack originally cost?.
Soda is on sale for $0.20 off each 12-pack. A man bought 4 12-packs and paid a total of $4.20. How much did each 12-pack originally cost?.
Maths-General