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Mathematical Reasoning
hard
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?
A
$\left( { \sim P} \right) \vee \left( {Q \wedge R} \right)$
B
$\left( {P \wedge Q} \right) \vee \left( { \sim R} \right)$
C
$\left( { \sim P} \right) \wedge \left( { \sim Q \wedge R} \right)$
D
$P \vee \left( { \sim Q \wedge R} \right)$
(JEE MAIN-2019)
Solution
$P$ is True
$Q$ is False
$R$ is True
$\therefore \sim Q$ is True
$ \sim Q \wedge R$ is True
$\therefore P \vee \left( { \sim Q \wedge R} \right)$ is True.
Standard 11
Mathematics
