prep - 101: If xy + z = x(y + z), which of the following must be true?

ad264

    

If xy + z = x(y + z), which of the
following must be true?

    

 

    

(A) x = 0 and z = 0

    

(B) x = 1 and y = 1

    

(C) y = 1 and z = 0

    

(D) x = 1 or y = 0

    

(E) x = 1 or z = 0

Ans: E

我有看前人帖子知道E怎样判断

请问将A代入，式子不是也成立 0 = 0

是那边不true？

Tracylee03

关键A中是and也就是说X=0 且Z=0 ,式子才成立.应该用or来表达.

whytou

a is not a "must be true".

if z = 0, x could be anything and the equation still holds.

xy+z = xy+xz

z=xz

for z = xz, its must be true that either z=0 (and x can be anything), or x=1 (and z can be anything)

ad264

谢谢两位解释！了解了。