Question

Select the expression that is equivalent to (x+yˉ)z.

a. x+y+zˉ
b. x+yˉ+z
c. x+yˉ+zˉ
d. x+yˉ+zˉ

Answer 1

The expression equivalent to
`(x + \overline y )z` is x +
`\overline y \overline z`, and the correct option is d: x +
`\overline y \overline z`. This reflects the logical OR of x and the logical AND of the negations of y and z.

The expression (x +
`\overline y`)z can be expanded as xz +
`\overline y`z. Comparing this with the provided options, the equivalent expression is x +
`\overline y \overline z`. In option d, x +
`\overline y \overline z`, the negation (overline) applies to both y and z, capturing the logical AND operation.

This expression represents the logical OR of x and the logical AND of
`\overline y` and
`\overline z.` The other options do not match this structure. Thus, the correct choice is option d: x +
`\overline y \overline z`, reflecting the original expression's logic where x is combined with the negation of y and z through logical AND.