$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to 

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements

$(i)$ $p \leftrightarrow  q$ 

$(ii)$ $~ p \leftrightarrow q$

$(iii)$ $~ q \leftrightarrow p$

$(iv)$ $~ p \leftrightarrow ~ q$

Negation of statement "If I will go to college, then I will be an engineer" is -

If $\left( {p \wedge  \sim q} \right) \wedge \left( {p \wedge r} \right) \to  \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

$(p \to q) \leftrightarrow (q\ \vee  \sim p)$ is