The statement $B \Rightarrow((\sim A ) \vee B )$ is equivalent to
$B \Rightarrow( A \Rightarrow B )$
$A \Rightarrow( A \Leftrightarrow B )$
$A \Rightarrow((\sim A ) \Rightarrow B )$
$B \Rightarrow((\sim A ) \Rightarrow B )$
Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$
If the truth value of the Boolean expression $((\mathrm{p} \vee \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r}) \wedge(\sim \mathrm{r})) \rightarrow(\mathrm{p} \wedge \mathrm{q}) \quad$ is false then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ respectively can be:
$\sim (p \vee q)$ is equal to
Which of the following is not a statement
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?