JEE Main Solved Paper 2017 Question 4

Question: The following statement $ (p\to q)\to [(\tilde{\ }p\to q)\to q] $ is: JEE Main Solved Paper-2017

Options:

A) a fallacy

B) a tautology

C) equivalent to $ \tilde{\ }p\to q $

D) equivalent to $ p\to -q $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ (p\to q)[(\tilde{\ }p\to q)\to q] $
p q $\tilde{\ }p$ $p\to q $ $\tilde{\ }p\to q$ $(\tilde{\ }p\to q)\to q$ $(p\to q)\to ((\tilde{\ }p\to q)\to q)$
T F F F T F T
T T F T T T T
F F T T F T T
F T T T T T T

$ \therefore $ It is tautology