Manpreet Singh wrote: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
B. y = 1 and z = 0
D. x = 1 or y = 0
E. x = 1 or Z = 0
Try to show that four of the five answer choices DON'T have to be true.
Answer choice A states that BOTH x and z must be equal to 0.
If we substitute z=0 into xy+z = x(y+z), we get:
xy + 0 = x(y+0)
xy = xy.
The resulting equation suggests that -- if z=0 -- then x and y can be ANY VALUES.
Thus, the following combination satisfies xy+z = x(y+z):
x=2, y=2, z=0.
Eliminate A, since it doesn't have to be true that x=0 and z=0.
Eliminate B, since it doesn't have to be true that x=1 and y=1.
Eliminate C, since it doesn't have to be true that y=1 and z=0.
Eliminate D, since it doesn't have to be true that x=1 or y=0.
The correct answer is
E.
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