Let $F_{1}(A, B, C)=(A \wedge \sim B) \vee[\sim C \wedge(A \vee B)] \vee \sim A$ and $F _{2}( A , B )=( A \vee B ) \vee( B \rightarrow \sim A )$ be two logical expressions. Then ...... .
$F _{1}$ and $F _{2}$ both are tautologies
$F _{1}$ is a tautology but $F _{2}$ is not a tautology
$F _{1}$ is not tautology but $F _{2}$ is a tautology
Both $F _{1}$ and $F _{2}$ are not tautologies
Which of the following is an open statement
Which of the following is true
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 statement 'If Jaipur is capital of Rajasthan, then Jaipur is in India' is
For integers $m$ and $n$, both greater than $1$ , consider the following three statements
$P$ : $m$ divides $n$
$Q$ : $m$ divides $n^2$
$R$ : $m$ is prime,
then true statement is