A) \[(\tilde{\ }p\vee \tilde{\ }q)\vee (p\vee \tilde{\ }q)\]
B) \[(p\to q)\vee (p\wedge \tilde{\ }q)\]
C) \[(\tilde{\ }p\wedge q)\wedge (\tilde{\ }q)\]
D) \[(\tilde{\ }p\wedge q)\vee (\tilde{\ }q)\]
Correct Answer: C
Solution :
[c] We consider following truth table.| \[p\] | \[q\] | \[\tilde{\ }p\] | \[\tilde{\ }q\] | \[p\wedge q\] | \[p\vee q\] | \[(\tilde{\ }(p\vee q)\] | \[(p\wedge q)\wedge \]\[(\tilde{\ }(p\vee q)\] |
| T | T | F | F | T | T | F | F |
| T | F | F | T | F | T | F | F |
| F | T | T | F | F | T | F | F |
| F | F | T | T | F | F | T | F |
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