Mathematical Logic And Boolean Algebra Question 74
Question: The negation of $ (p\vee \tilde{\ }q)\wedge q $ is
Options:
A) $ (\tilde{\ }p\vee q)\wedge \tilde{\ }q $
B) $ (p\wedge \tilde{\ }q)\vee q $
C) $ (\tilde{\ }p\wedge q)\vee \tilde{\ }q $
D) $ (p\wedge \tilde{\ }q)\vee \tilde{\ }q $
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Answer:
Correct Answer: C
Solution:
[c] $ \tilde{\ }{(p\vee (\tilde{\ }q))\wedge q}=(\tilde{\ }(p\vee (\tilde{\ }q)))\vee (\tilde{\ }q) $ By De Morgan?s Law, $ \tilde{\ }(A\wedge B)=(\tilde{\ }A)\vee (\tilde{\ }B) $ $ =((\tilde{\ }p)\wedge (\tilde{\ }(\tilde{\ }q)))\vee (\tilde{\ }q) $ [Using De Morgan?s law again] $ =(\tilde{\ }p\wedge q)\vee (\tilde{\ }q) $ $ [\because \tilde{\ }(\tilde{\ }q)=q] $
BETA
