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 $