推 JiaJiaH:真是太感謝了!! 原來是這樣ㄚ~~~ 解答了我心中的困惑... 01/18 12:09
推 surfingdream:thx a lot 01/18 13:27
※ 引述《surfingdream (GMATing)》之銘言：
: 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
: III)(a@b)@c =a@(b@c)
: 請問一下上面這個怎麼算出來是true
: 感謝
原式a@b=a+b-ab
(a@b)@C=a+b-ab+c-c(a+b-ab) =a+b+c-ab-ac-cb+abc
^^^^^^ ^ ^^^^^^^^^
表a b ab
(b@c)=b+c-bc
a@(b@c)=a+b+c-bc-a(b+c-bc) =a+b+c-bc-ab-ac+abc
^ ^^^^^^ ^^^^^^^^^
表a b ab
故成立
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