Mathematical Logic And Boolean Algebra Question 77
Question: Which of the following is true?
Options:
A) $ p\Rightarrow q\equiv \tilde{\ }p\Rightarrow \tilde{\ }q $
B) $ \tilde{\ }(p\Rightarrow \tilde{\ }q)\equiv \tilde{\ }p\wedge q $
C) $ \tilde{\ }(\tilde{\ }p\Rightarrow \tilde{\ }q)\equiv \tilde{\ }p\wedge q $
D) $ \tilde{\ }(\tilde{\ }p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)] $
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Answer:
Correct Answer: C
Solution:
[c] $ \tilde{\ }(p\Rightarrow q)\equiv p\wedge \tilde{\ }q $
$ \therefore \tilde{\ }(\tilde{\ }p\Rightarrow \tilde{\ }q)\equiv \tilde{\ }p\wedge \tilde{\ }(\tilde{\ }q)\equiv \tilde{\ }p\wedge q $ Thus $ \tilde{\ }(\tilde{\ }p\Rightarrow \tilde{\ }q)\equiv ,\tilde{\ }p\wedge q $
BETA
