1. ⇒ (MHT CET 2023 12th May Evening Shift )

Let

Statement 1 : If a quadrilateral is a square, then all of its sides are equal.

Statement 2: All the sides of a quadrilateral are equal, then it is a square.

A. Statement 2 is contrapositive of statement 1.

B. Statement 2 is negation of statement 1.

C. Statement 2 is inverse of statement 1.

D. Statement 2 is the converse of statement 1.

Correct answer option is (D)

Let $p$ : A quadrilateral is a square

$q :$ All sides of quadrilateral are equal.

$∴$ Statement 1 is $p \to q$ ,

Statement 2 is $q \to p$

$∴$ Statement 2 is the converse of statement 1.

2. ⇒ (MHT CET 2023 12th May Morning Shift )

The inverse of the statement "If the surface area increase, then the pressure decreases.", is

A. If the surface area does not increase, then the pressure does not decrease.

B. If the pressure decreases, then the surface area increases.

C. If the pressure does not decreases, then the surface area does not increase.

D. If the surface area does not increase, then the pressure decreases.

Correct answer option is (A)

Let $p$ : The surface area increases

$q :$ The pressure decreases

Given statement is $p \to q$

$∴$ It's inverse is $\sim p \to\sim q$

$∴$ Option (A) is correct.

3. ⇒ (MHT CET 2023 12th May Morning Shift )

The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd, then both $x$ and $y$ are odd" is

A. If both $x$ and $y$ are odd integers, then $x y$ is odd.

B. If both $x$ and $y$ are even integers, then $x y$ is even.

C. If $x$ or $y$ is an odd integer, then $x y$ is odd.

D. If both $x$ and $y$ are not odd integers, then the product $x y$ is not odd.

Correct answer option is (D)

Let $p : x$ and $y$ are integers such that $x y$ is odd.

$q :$ both $x$ and $y$ are odd.

$∴$ Given statement is $p \to q$

$∴$ Its contrapositive is $\sim q \to p$

$∴$ Option (D) is correct.

⇒ Mathematical Logic