JEE Main 12 Jan 2019 Evening Question 2
Question: The expression $ \tilde{\ }(\tilde{\ }p\to q) $ is logically equivalent to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
Options:
A) $ p\wedge q $
B) $ \tilde{\ }p\wedge q $
C) $ \tilde{\ }p\wedge \tilde{\ }q $
D) $ p\wedge \tilde{\ }q $
Show Answer
Answer:
Correct Answer: C
Solution:
| $ p $ | $ \tilde{\ }p $ | $ q $ | $ \tilde{\ }q $ | $ \tilde{\ }p\to q $ | $ \tilde{\ }(\tilde{\ }p\to q) $ | $ (\tilde{\ }p\wedge \tilde{\ }q) $ |
|---|---|---|---|---|---|---|
| T | F | T | F | T | F | F |
| F | T | T | F | T | F | F |
| T | F | F | T | T | F | F |
| F | T | F | T | F | T | T |
Above truth table shows that $ (\tilde{\ }p\to q) $ is logically equivalent to $ (\tilde{\ }p\wedge \tilde{\ }q) $ .
