A) \[S(p,q,r)\]
B) \[\sim S(\sim p,\sim q,\sim r)\]
C) \[\sim S\,(p,q,r)\]
D) \[S*\,(p,q,r)\]
Correct Answer: C
Solution :
| \[S\,(p,q,r)=\,\tilde{\ }p\wedge [\tilde{\ }(q\vee r)]\] |
| So, \[S\,(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\equiv \,\tilde{\ }(\tilde{\ }p)\wedge [\tilde{\ }(\tilde{\ }q\vee \tilde{\ }r)]\]\[\equiv p\wedge (q\vee r)\] |
| \[S*(p,q,r)\equiv \,\tilde{\ }p\vee [\tilde{\ }q\wedge r)]\] |
| \[S*(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\equiv p\vee (q\vee r)\] |
| Clearly, \[S*(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\equiv \,\,\tilde{\ }S(p,q,r)\] |
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