Consider the following three statements $P: 11$ is a prime number. Q: 7 is a factor of 176 . $R$ : LCM of 3…
Consider the following three statements
$P: 11$ is a prime number.
Q: 7 is a factor of 176 .
$R$ : LCM of 3 and 7 is 21 .
Then, the truth value of which one of the following statement is true?
$P \vee(\sim Q \wedge R)$
$(\sim P) \wedge(\sim Q \wedge R)$
$(P \wedge Q) \vee(\sim R)$
$(\sim P) \vee(Q \wedge R)$
Solution
$P: 11$ is a prime number $(\mathrm{T})$
$Q: 7$ is a factor of $176(\mathrm{~F})$
$R$ : L.C.M of 3 and 7 is 21 (T)
Now, $P \vee(\sim Q \wedge R) \equiv \mathrm{T} \vee(\mathrm{T} \wedge \mathrm{T}) \equiv \mathrm{T}$