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Question

For an integer n, a student states the following:
I. If n is odd, (n+1)2 is even
II. If n is even, (n1)2 is odd
III. If n is even, n1 is irrational.
Which of the above statements would be true?


A

I and III

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B

I and II

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C

I, II and III

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D

II and III

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Solution

The correct option is B

I and II


x is defined for a number x only if x is positive.
I - If n is odd, then n+1 is even, which implies that (n+1)2 is even.
II - If n is even, then n1 is odd, which implies that (n1)2 is odd.
III - If (n - 1) < 0 then n1 is not defined. Thus, this statement is false.

Hence, I and II are the two corrrect statements.


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