PP PS 1 Q176

[nemolee]

176. 18407-!-item-!-187;#058&011575
If the operation ⊙ is defined for all integers a and b by a ⊙ b = a + b - ab which of the following statements must be true for all integers a, b, and c ?
I. a ⊙ b = b ⊙ a
II. a ⊙ 0 = a
III. ( a ⊙ b ) ⊙ c = a ⊙ ( b ⊙ c )
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
ANS: E

自己選到了 ( error : c )... .冷汗又滴了兩下

對I, II 都沒有問題，可是，為什麼 III. 也可以?

謝謝

[amazingslim]

( a ⊙ b ) ⊙ c=(a+b-ab) ⊙ c=a+b+c-ab-(ac+bc-abc)

a ⊙ ( b ⊙ c ) =a ⊙(b+c-bc)=a+b+c-bc-(ab+ac-abc)

[nemolee]

多謝 amaz 大，一出手，讓我無言....