| Consider the following three statements: |
| P : 5 is a prime number. |
| Q : 7 is a factor of 192. |
| R : L.C.M.of5 and 7 is 35. |
| Then the truth value of which one of the following statements is true? |
A) \[(\tilde{\ }P)\vee (Q\wedge R)\]
B) \[(P\wedge Q)\vee (\tilde{\ }R)\]
C) \[(\tilde{\ }P)\wedge (\tilde{\ }Q\wedge R)\]
D) \[P\vee (\tilde{\ }Q\wedge R)\]
Correct Answer: D
Solution :
| P is True |
| Q is False |
| R is True |
| \[\therefore \]\[\tilde{\ }Q\]is True |
| \[\tilde{\ }Q\wedge R\]is True |
| \[\therefore \]\[\tilde{\ }Q\wedge R\]is True. |
| \[\therefore \]\[P\vee (\tilde{\ }Q\wedge R)\] is True. |
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