Mathematical Logic And Boolean Algebra Question 35

Question: Which of the following is logically equivalent to $ \tilde{\ }(\tilde{\ }p\Rightarrow q) $

Options:

A) $ p\wedge q $

B) $ p\wedge \tilde{\ }q $

C) $ \tilde{\ }p\wedge q $

D) $ \tilde{\ }p\ \wedge \tilde{\ }q $

Show Answer

Answer:

Correct Answer: D

Solution:

Since $ \tilde{\ }(p\Rightarrow q)\equiv p\ \wedge \tilde{\ }q $ $ \tilde{\ }(\tilde{\ }p\Rightarrow q)=\ \tilde{\ }p\ \wedge \tilde{\ }q $