JEE Main 12 Jan 2019 Morning Question 9
Question: The Boolean expression $ ((p\wedge q)\vee (p\vee \tilde{\ }q)) $ $ \wedge (\tilde{\ }p\wedge \tilde{\ }q) $ is equivalent to [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) $ (\tilde{\ }p)\wedge (\tilde{\ }q) $
B) $ p\wedge (\tilde{\ }q) $
C) $ p\wedge q $
D) $ p\vee (\tilde{\ }q) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ ((p\wedge q)\vee (p\vee \tilde{\ }q))\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv ((p\vee (p\vee \tilde{\ }q))\wedge (q\vee \tilde{\ }q)))\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv ((p\vee \tilde{\ }q)\wedge (q\vee \tilde{\ }q\vee p))\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv ((p\vee \tilde{\ }q)\wedge (t\vee p))\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv ((p\vee \tilde{\ }q)\wedge t)\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv (p\vee \tilde{\ }q)\wedge (\tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv (p\wedge \tilde{\ }p\wedge \tilde{\ }q)\vee (\tilde{\ }q\wedge \tilde{\ }p\wedge \tilde{\ }q) $ $ \equiv (c\wedge \tilde{\ }q)\vee (\tilde{\ }q\wedge \tilde{\ }p) $ $ \equiv c\vee (\tilde{\ }q\wedge \tilde{\ }p) $ $ \equiv \tilde{\ }p\wedge \tilde{\ }q $
