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单选题
Which of the following must be true?I. a Φ b=b Φ aII. a Φ (a + 1) = a2III. a/2 Φ b/2 = aΦb/2
A

I only

B

II only

C

III only

D

I and III only

E

II and III only

参考答案

参考解析
解析：
Determine whether each Roman numeral equation is true or false when a Φ b = ab - a.
~ I. Since b Φ a = ab－b and ab－a is not necessarily equal to ab－b, a Φ b = b Φ a is not always true. Equation I need not be true.
~ II. To evaluate a Φ (a + 1), let b = a + 1: a Φ (a + 1) = a (a + 1)-a =a2 + a－a = a2. Hence, equation II must be true.
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