Maths-
General
Easy

Question

A student was asked to prove a statement by induction. He proved
i) P(5) is true and
ii) truth of P(n)rightwards double arrow truth of P(n+1), n element of N.
On the basis of this, he could conclude that P(n) is true

  1. for no n    
  2. for all n greater or equal than 5    
  3. for all n    
  4. nothing can be said    

hintHint:

Consider a statement P(n), where n is a natural number. Then to determine the validity of P(n) for every n, use the following principle:
Step 1:  Check whether the given statement is true for n = 1.
Step 2: Assume that given statement P(n) is also true for n = k, where k is any positive integer.
Step 3:  Prove that the result is true for P(k+1) for any positive integer k.
If the above-mentioned conditions are satisfied, then it can be concluded that P(n) is true for all n natural numbers.

The correct answer is: for all n greater or equal than 5


    By induction the student proved:

    i) P(5) is true and
    ii) truth of P(n)rightwards double arrow truth of P(n+1), n element of N.
    rightwards double arrow space P left parenthesis 5 right parenthesis space space equals space P left parenthesis 6 right parenthesis space left parenthesis space F r o m space s t a t e m e n t space 2 right parenthesis
rightwards double arrow P left parenthesis 6 right parenthesis space equals space P left parenthesis 7 right parenthesis
rightwards double arrow P left parenthesis 7 right parenthesis space equals space P left parenthesis 8 right parenthesis
B u t comma space t h e space r e v e r s e space c a n n o t space b e space s a i d space f o r space t h e space s a m e space colon space i. e
w e space c a n n o t space p r o v e space b y space t h e s e space s t a t e m e n t s space t h a t space P left parenthesis n right parenthesis space equals space P left parenthesis n minus 1 right parenthesis
    Thus, by conclusion P(n) is true for all n greater or equal than 5

    Related Questions to study

    General
    physics

    Orbital velocity of an artificial satellite does not depend upon.

    Orbital velocity of an artificial satellite does not depend upon.

    physicsGeneral
    General
    Physics

    A satellite is moving around the earth with speed v in a circular orbit of radius .i If the orbit radius is decreasd by 1% its speed will

    A satellite is moving around the earth with speed v in a circular orbit of radius .i If the orbit radius is decreasd by 1% its speed will

    PhysicsGeneral
    General
    biology

    Which of the following is used to normalize low level heart beats

    Which of the following is used to normalize low level heart beats

    biologyGeneral
    parallel
    General
    physics

    If the height of a satellite from the earth is negligible in comparison of the radius of the earth R, the orbital velocity of the satellite is……

    If the height of a satellite from the earth is negligible in comparison of the radius of the earth R, the orbital velocity of the satellite is……

    physicsGeneral
    General
    physics

    A satellite revolves around the earth in an elliptical orbit. Its speed,

    A satellite revolves around the earth in an elliptical orbit. Its speed,

    physicsGeneral
    General
    biology

    Cross section image of internal body structure can be obtained by using this medical technique

    Cross section image of internal body structure can be obtained by using this medical technique

    biologyGeneral
    parallel
    General
    Maths-

    If there is an error of 0.02 sq. cm is made in calculating the area of a circle. If the radius is 5cm, then the percentage error in the circumference of the circle is

    If there is an error of 0.02 sq. cm is made in calculating the area of a circle. If the radius is 5cm, then the percentage error in the circumference of the circle is

    Maths-General
    General
    chemistry-

    Rubber latex is which type of emulsion

    Rubber latex is which type of emulsion

    chemistry-General
    General
    physics

    A small satellite is revolving near earth's surface. Its orbital velocity will be nearly=...kms-1

    A small satellite is revolving near earth's surface. Its orbital velocity will be nearly=...kms-1

    physicsGeneral
    parallel
    General
    physics

    Two  satellites A and B go round a planet p in circular orbits having radii 4R and R  respectively if the speed of the satellite A is 3V , the speed if satellite B will be

    Two  satellites A and B go round a planet p in circular orbits having radii 4R and R  respectively if the speed of the satellite A is 3V , the speed if satellite B will be

    physicsGeneral
    General
    biology

    An endoscope is employed by a physician to view the internal parts of a body organ. It is based on the principle is

    An endoscope is employed by a physician to view the internal parts of a body organ. It is based on the principle is

    biologyGeneral
    General
    biology

    The most abundant source of protons in the body are

    The most abundant source of protons in the body are

    biologyGeneral
    parallel
    General
    physics

    The period of a satellite in circular orbit around a planet is Independent of

    The period of a satellite in circular orbit around a planet is Independent of

    physicsGeneral
    General
    biology

    Assertion : Sometimes nonsmokers are prone to lung cancer.
    Reason : Nonsmokers are also called passive smokers.

    Assertion : Sometimes nonsmokers are prone to lung cancer.
    Reason : Nonsmokers are also called passive smokers.

    biologyGeneral
    General
    physics

    As astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will

    As astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will

    physicsGeneral
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.