A) \[(P\wedge r)\,\wedge \tilde{\ }q\]
B) \[(\tilde{\ }P\wedge \tilde{\ }q)\wedge r\]
C) \[\tilde{\ }P\vee r\]
D) \[(P\wedge \tilde{\ }q)\vee r\]
Correct Answer: A
Solution :
| \[\tilde{\ }(\tilde{\ }p\vee q)\wedge (p\wedge r)\cap (\tilde{\ }q\wedge r)\] |
| \[\equiv \,\,[(p\wedge \tilde{\ }q)\vee (P\wedge r)]\wedge (\tilde{\ }q\wedge r)\] |
| \[\equiv [p\wedge (\tilde{\ }q\vee r)]\wedge (\tilde{\ }q\wedge r)\] |
| \[\equiv p\wedge (\tilde{\ }q\wedge r)\] |
| \[\equiv (p\wedge r)\tilde{\ }q.\] |
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