单选题If a and b are integers and the sum of ab and b is even, which of the following could be true?Ⅰ. a and b are both odd.Ⅱ. a is even and b is odd.Ⅲ. a is odd and b is even.AⅠ onlyBⅡonlyCⅢ onlyDⅠ and ⅡEⅠand Ⅲ
单选题
If a and b are integers and the sum of ab and b is even, which of the following could be true?Ⅰ. a and b are both odd.Ⅱ. a is even and b is odd.Ⅲ. a is odd and b is even.
A
Ⅰ only
B
Ⅱonly
C
Ⅲ only
D
Ⅰ and Ⅱ
E
Ⅰand Ⅲ
参考解析
解析：
Plug-in. StatementⅠ：if a and b are both odd, says a=1 and b=3, then ab+b=6. Since the sum is even, statementⅠ is true. StatementⅡ：1et a=2 and b=3, then ab+b=9. Since the sum is odd, this statement is false. Statement Ⅲ：let a=3 and b=2, then ab+b=8, which is even. So both statement Ⅰand statementⅢ are true.
Plug-in. StatementⅠ：if a and b are both odd, says a=1 and b=3, then ab+b=6. Since the sum is even, statementⅠ is true. StatementⅡ：1et a=2 and b=3, then ab+b=9. Since the sum is odd, this statement is false. Statement Ⅲ：let a=3 and b=2, then ab+b=8, which is even. So both statement Ⅰand statementⅢ are true.
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