Mathematical Logic And Boolean Algebra Question 11
Question: $ (p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q) $ is
[Karnataka CET 2003]
Options:
A) A tautology
B) A contradiction
C) Both a tautology and a contradiction
D) Neither a tautology nor a contradiction
Show Answer
Answer:
Correct Answer: B
Solution:
$ (p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)=(p\ \wedge \tilde{\ }p)\wedge (\tilde{\ }q\wedge q)=f\wedge f=f $ . (By using associative laws and commutatine laws) \ $ (p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q) $ is a contradiction.
BETA
