# Converse and contrapositive

• Dec 1st 2008, 12:03 PM
booper563
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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• Dec 1st 2008, 12:26 PM
masters
Quote:

Originally Posted by booper563
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)

Please help me this question is worth 4 points and I am not sure what to do.
Or write

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