Both c. x+ yˉ + zˉ and d. x+ yˉ + zˉ are equivalent to (x+ yˉ)z.
Let's analyze each option:
a. x+y + zˉ: This expands to xz + yzˉ + y. This is not equivalent to (x+ yˉ)z because it includes y, which is not present in the original expression.
b. x+ yˉ+z: This expands to xz + yzˉ + z. This is similar to option a but includes z instead of y. Again, it is not equivalent to the original expression because it includes z outside the parentheses.
c. x+ yˉ + zˉ: This expands to xz + yzˉ + zˉ. This option includes both yˉ and zˉ as required. Additionally, it multiplies each term by z, which is also necessary.
d. x+ yˉ + zˉ: This is identical to option c and therefore also expands to xz + yzˉ + zˉ.
Therefore, both c. x+ yˉ + zˉ and d. x+ yˉ + zˉ are equivalent to (x+ yˉ)z.