Write the contrapositive and converse of the following statement:
$x$ is an even number implies that $x$ is divisible by $4.$
$x$ is an even number implies that $x$ is divisible by $4.$
(N/A) The given statement is: If $x$ is an even number,then $x$ is divisible by $4.$
$1$. The contrapositive is: If $x$ is not divisible by $4,$ then $x$ is not an even number.
$2$. The converse is: If $x$ is divisible by $4,$ then $x$ is an even number.
$1$. The contrapositive is: If $x$ is not divisible by $4,$ then $x$ is not an even number.
$2$. The converse is: If $x$ is divisible by $4,$ then $x$ is an even number.
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Similar Questions
Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.
Consider the following statements:
$P$: $I$ have fever
$Q$: $I$ will take medicine
$R$: $I$ will take rest
The statement "If $I$ have fever,then $I$ will take medicine and $I$ will take rest" is equivalent to:
$P$: $I$ have fever
$Q$: $I$ will take medicine
$R$: $I$ will take rest
The statement "If $I$ have fever,then $I$ will take medicine and $I$ will take rest" is equivalent to:
DifficultJEE MAIN 2023
View SolutionIf the statement $p \rightarrow (q \vee r)$ is false,then the truth values of $p, q, r$ are respectively:
Medium
View SolutionThe negation of $(p \land q) \to ((p \lor r) \to \sim q)$ is equivalent to ...
DifficultMHT CET 2026
View SolutionAmong the statements:
$(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$ is a tautology
$(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction
$(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$ is a tautology
$(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction
DifficultJEE MAIN 2023
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