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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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Answers (2)
  1. 29 August, 06:21
    0
    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 ".
  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).
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