Let * be defined as x * y = x' + y. Let z = x * y. Value of z * x is

The problem defines a custom operation (*) as: x * y = x' + y (which is equivalent to the logical implication x -> y)

We are given: z = x * y = x' + y

Now, we need to find the value of: z * x

Using the definition of the operation (*), we substitute z as the first operand and x as the second operand: z * x = z' + x

Now, substitute the value of z (which is x' + y) into this expression: z * x = (x' + y)' + x

Apply De Morgan's Law to simplify the term (x' + y)': (x' + y)' = (x'') * y' = x * y'

Substitute this back into the equation: z * x = (x * y') + x

Apply the Distributive Law of Boolean algebra [A + (B * C) = (A + B) * (A + C)]: (x * y') + x = x + (x * y') = (x + x) * (x + y') = x * (x + y') = x

Alternatively, you can use the Absorption Law [A + (A * B) = A]: x + (x * y') = x

Therefore, the final simplified value of z * x is x.