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
