If p: , n N , n^2+n is an even number q: , n N , n^2-n is an odd number, then the truth values of p q, p q and p q are respectively

MHT CET 2022 Mathematics question

Not in JEE syllabus

If is an even number is an odd number, then the truth values of , and are respectively

(A)F, T, T
(B)F, F, T
(C)F, T, FCorrect
(D)T, T, F

Answer: (C)

Solution

is a product of two consecutive integers, hence always even, so is true. is also a product of two consecutive integers, hence always even, so " is odd" is false for every and is false. Therefore T F

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Question ID VK-097038