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28 August, 18:04

If two circle have the same diameter, then they have the same circumference.

Write the converse, inverse and contrapositive statement for the sentence.

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  1. 28 August, 19:36
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    Converse: If the circumference of the two circle is same then they have same diameter.

    Inverse: If two circle do not have same diameter then they do not have same circumference.

    Contrapositive: If two circle do not have same circumference then they do not have same diameter.

    Step-by-step explanation:

    Let the statement's be,

    p : Two circles have same diameter.

    q : Two circles have same circumference.

    The given statement is a conditional statement logically is given as

    p → q

    It means p implies q, that is if p then q

    where p is called antecedent or hypothesis and

    q is called consequent or conclusion.

    The converse of this statement logically is given as

    q → p

    It means q implies p, that is If q then p.

    Converse: If the circumference of the two circle is same then they have same diameter.

    The Inverse of this statement logically is given as

    ~p → ~q

    It means negation p implies negation q, that is If not p then not q.

    Inverse: If two circle do not have same diameter then they do not have same circumference.

    The Contrapositive of this statement logically is given as

    ~q → ~p

    It means negation q implies negation p, that is If not q then not p.

    Contrapositive: If two circle do not have same circumference then they do not have same diameter.
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