Mathematical Logic And Boolean Algebra Question 69
Question: $ (p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q) $ is
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:
[b] $ (p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)=(p\wedge \tilde{\ }q)\wedge (\tilde{\ }q\wedge q) $ $ =f\wedge f=f $ (By using associative laws and commutative laws)
$ \therefore (p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q) $ is a contradiction.
BETA
