For all integers \(a\) and \(b\text{,}\) if \(a\) or \(b\) is not even, then \(a+b\) is not even.
For all integers \(a\) and \(b\text{,}\) if \(a\) and \(b\) are even, then \(a+b\) is even.
There are numbers \(a\) and \(b\) such that \(a+b\) is even but \(a\) and \(b\) are not both even.
False. For example, \(a = 3\) and \(b = 5\text{.}\) \(a+b = 8\text{,}\) but neither \(a\) nor \(b\) are even.
False, since it is equivalent to the original statement.
True. Let \(a\) and \(b\) be integers. Assume both are even. Then \(a = 2k\) and \(b = 2j\) for some integers \(k\) and \(j\text{.}\) But then \(a+b = 2k + 2j = 2(k+j)\) which is even.
True, since the statement is false.