 Mathematics
29 August, 05:56

# 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.

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1. 29 August, 06:21
0

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 ".
2. 29 August, 06:21
0
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).