The statment $ \sim \left( {p \leftrightarrow \sim q} \right)$ is
Equivalent to $p \leftrightarrow q$
'Equivalent to $ \sim p \leftrightarrow q$
A tautalogy
A fallacy
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?
The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:
Negation of statement "If I will go to college, then I will be an engineer" is -
Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements
$(i)$ $p \leftrightarrow q$
$(ii)$ $~ p \leftrightarrow q$
$(iii)$ $~ q \leftrightarrow p$
$(iv)$ $~ p \leftrightarrow ~ q$
If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?