Which of the following Venn diagram corresponds to the statement “All mothers are women” ($M$ is the set of all mothers, $W$ is the set of all women)
If $p, q, r$ are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true then
$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to
Consider the following statements :
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
The contrapositive of $(p \vee q) \Rightarrow r$ is
If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.