xy + z = x(y +z)If xy + z = x(y + z), which of the following must be true:
1. x = 0 and z = 0
2. x = 1 and y = 1
3. y = 1 and z = 0
4. x = 1 or y = 0
5. x = 1 or z = 0
xy + z = xy + xz
z = xz
z - xz = 0
z(1 - x) = 0.
For the resulting equation to be valid, either z=0 or x=1.
The correct answer is E.
A is incorrect because if z=0, then x can be ANY VALUE.
Thus, it does NOT have to be true that z=0 AND x=0.
For example, it is possible that z=0 and x=1.
B and C are incorrect because -- when the equation is simplified -- it no longer includes y.
The implication is that y can be ANY VALUE.
Thus, it does NOT have to be true that y=1.
For example:
It is possible that x=1 and y=2, proving that B does not have to be true.
It is possible that z=0 and y=2, proving that C does not have to be true.
