The statment $ \sim \left( {p \leftrightarrow  \sim q} \right)$ is

  • A

    Equivalent to $p \leftrightarrow q$

  • B

    'Equivalent to $ \sim p \leftrightarrow q$

  • C

    A tautalogy

  • D

    A fallacy

Similar Questions

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?

  • [JEE MAIN 2019]

The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:

  • [JEE MAIN 2021]

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?

  • [JEE MAIN 2021]