Consider the following statement:
Statement A: ? integers m and n, if 2m + n is odd then m and n are both odd.
(a) Write a negation for Statement A.
(b) Disprove Statement A. That is, show that Statement A is false.
a. ? integers m and n such that 2m + n is odd and m and n are not both odd. In other words, ?
integers m and n such that 2m + n is odd and at least one of m and n is even.
b. Statement A can be shown to be false by giving a counterexample.
Counterexample: Let m = 1 and n = 2. Then 2m + n = 2 · 1 + 2 = 4, which is even, but it is not the
case that both m and n are odd because n is even.(This is one counterexample among many.)
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