(C) The contrapositive of a conditional statement $p \to q$ is defined as $\sim q \to \sim p$.Let $p$ be the statement: "The side of a square doubles.

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If the area of a square does not increase four times,then its side is not doubled.

(C) The contrapositive of a conditional statement $p \to q$ is defined as $\sim q \to \sim p$.Let $p$ be the statement: "The side of a square doubles."Let $q$ be the statement: "Its area increases four times."The contrapositive $\sim q \to \sim p$ is: "If the area of a square does not increase four times,then its side is not doubled."Thus,option $C$ is the correct answer.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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The contrapositive of the statement,"If the side of a square doubles,then its area increases four times",is

JEE MAIN 2016 All JEE MAIN

A
If the area of a square increases four times,then its side is not doubled.
B
If the area of a square increases four times,then its side is doubled.
C
If the area of a square does not increase four times,then its side is not doubled.
D
If the side of a square is not doubled,then its area does not increase four times.

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The contrapositive of the statement,"If the side of a square doubles,then its area increases four times",is

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Write the following statement in five different ways,conveying the same meaning.$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.

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Write the following statement in five different ways,conveying the same meaning.
$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.

Identify the type of "Or" used in the following statement and check whether the statement is true or false:
"$A$ rectangle is a quadrilateral or a $5$-sided polygon."

Write the negation of the following statement:
Both the diagonals of a rectangle have the same length.

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 $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.