A) \[(\sim p\wedge \sim q)\wedge r\]
B) \[(p\wedge \sim q)\vee r\]
C) \[\left( p\wedge r \right)\,\,\wedge \tilde{\ }\,q\]
D) \[\tilde{\ }p\wedge r\]
Correct Answer: C
Solution :
| p | q | R | \[\sim p\] | \[\sim p\vee q\] | \[\sim (\sim p\]\[\vee q\]) | \[(p\wedge q)\] | \[\sim q\] | \[\sim q\wedge r\] | \[[\sim (\sim p\vee q)\] \[\vee (q\vee r)]\] \[n(\sim q\wedge r)\] |
| T | T | T | F | T | F | T | F | F | F |
| T | T | F | F | T | F | F | F | F | F |
| T | F | T | F | F | T | T | T | T | T |
| T | F | F | F | F | T | F | T | F | F |
| F | T | T | T | T | F | F | F | F | F |
| F | T | F | T | T | F | F | F | F | F |
| F | F | T | T | T | F | F | T | T | F |
| F | F | F | T | T | F | F | T | F | F |
| \[(p\wedge r)\wedge \sim q\] |
| F F T F F F F F |
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