Mathematical Logic And Boolean Algebra Question 157

Question: The negative of $ q\ \vee \tilde{\ }(p\wedge r) $ is

[Karnataka CET 1997]

Options:

A) $ \tilde{\ }q\ \wedge \tilde{\ }(p\wedge r) $

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

C) $ \tilde{\ }q\vee (p\wedge r) $

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

$ \tilde{\ }(q\ \vee \tilde{\ }(p\wedge r))=\ \tilde{\ }q\wedge (\tilde{\ }(\tilde{\ }(p\wedge r))=\ \tilde{\ }q\wedge (p\wedge r) $ .