Mathematical Logic And Boolean Algebra Question 145
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{\ }(p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)] $
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Answer:
Correct Answer: C
Solution:
$ \tilde{\ }(p\Rightarrow q)\equiv p\ \wedge \tilde{\ }q $ \ $ \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
