Consider the following three statements :
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true ?
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true ?
Show Hint
- \((P \wedge Q) \vee (\sim R)\)
- \(P \vee (\sim Q \wedge R)\)
- \((\sim P) \wedge (\sim Q \wedge R)\)
- \((\sim P) \vee (Q \wedge R)\)
The Correct Option is B
Solution and Explanation
(1) \((P\wedge Q)\vee(\sim R) = (T\wedge F)\vee F = F\vee F = F\).
(2) \(P\vee(\sim Q\wedge R) = T\vee(T\wedge T) = T\).
(3) \((\sim P)\wedge(\sim Q\wedge R) = F\wedge T = F\).
(4) \((\sim P)\vee(Q\wedge R) = F\vee(F\wedge T) = F\).
Only (2) is true.
Answer: (2) \(P \vee (\sim Q \wedge R)\)
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