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Math Help - Converse and contrapositive

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    Converse and contrapositive

    write the converse and contrapositive of the following statement concerning whole numbers. Decide whether each of the three statements is true, and provide a counterexample for any statemetn that is not true.


    "If a and b are consecutive odd numbers, then a+b is an even number"




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    Quote Originally Posted by booper563 View Post
    write the converse and contrapositive of the following statement concerning whole numbers. Decide whether each of the three statements is true, and provide a counterexample for any statemetn that is not true.

    If p, then q is a conditional statement with a truth value
    If q, then p is its converse
    If ~p, then ~q is its inverse
    If ~q, then ~p is its contrapositive


    "If a and b are consecutive odd numbers, then a+b is an even number"

    P = "a and b are consecutive odd numbers"
    q = "a + b is an even number"

    If p, then q is true. So the contrapositive must be true since they are logically equivalent. The contrapositive says "If a + b is not an even number, then a and b are not consecutive odd numbers"

    The converse, If q, then p, is false since an even number does not have to be the sum of two consecutive odd numbers. The converse says "If a + b is an even number, then a and b are consecutive odd numbers".

    8 = 1 + 7 (8 is an even number, but 1 and 7 are not consecutive odd numbers)




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