Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”
If a number is not a prime then it is odd
If a number is not a prime then it is not odd
If a number is not odd then it is not a prime
If a number is not odd then it is a prime
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 number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)$ is True, is equal to
Consider the two statements :
$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology
$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.
Then :
The negation of the statement $''96$ is divisible by $2$ and $3''$ is
If $p \to ( \sim p\,\, \vee \, \sim q)$ is false, then the truth values of $p$ and $q$ are respectively .