Which statement is the inverse of the following?

"If a polygon has four sides, then it is called a quadrilateral."

A. If a quadrilateral has four sides, then it is called a polygon.

B. If a polygon is called a quadrilateral, then it has four sides.

C. If a polygon is not called a quadrilateral, then it does not have four sides.

D. If a polygon does not have four sides, then it is not called a quadrilateral.

Question

Mathematics

Alexia Hampton

20 August, 15:03

Which statement is the inverse of the following?

"If a polygon has four sides, then it is called a quadrilateral."

A. If a quadrilateral has four sides, then it is called a polygon.

B. If a polygon is called a quadrilateral, then it has four sides.

C. If a polygon is not called a quadrilateral, then it does not have four sides.

D. If a polygon does not have four sides, then it is not called a quadrilateral.

+3

Answers (2)

Know the Answer?

Trystan · Answer 1

The best answer is "D"

If a polygon does not have four sides, then it is not called a quadrilateral.

Explanation:

If P ⇒ Q is a statement, then the inverse of this statement is:

not Q ⇒ not P.

A statement and its inverse are equivalent.

For the statement:

"If a polygon has four sides, then it is called a quadrilateral."

The inverse is " If a polygon does not have four sides, then it is not called a quadrilateral ".

Carissa Singh · Answer 2

C. If a polygon is not called a quadrilateral, then it does not have four sides.

Step-by-step explanation:

If P ⇒ Q is a statement, then the contra positive of this statement is:

not Q ⇒ not P.

A statement and its contra positive are equivalent.

The given statement is:

"If a polygon has four sides, then it is called a quadrilateral."

The contra positive of the above is:

"If a polygon is not called a quadrilateral, then it does not have four sides" which is given in (C).

Hence, the correct option is (C).