The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to
$(\sim x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge \sim y) \vee(\sim x \wedge y)$
$(x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge y) \wedge(\sim x \vee \sim y)$
The number of values of $r \in\{p, q, \sim p , \sim q \}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is:
If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively
Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is
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?
Which of the following statement is true