The sum of products expansion for the function
$F(x, y, z) = (x + y)\bar z$ is given as

Question

The sum of products expansion for the function $F(x, y, z) = (x + y)\bar z$ is given as

Accepted Answer

Correct answer: D — Goal: write F(x,y,z) = (x + y) z̄ as a sum of products (minterm) expansion. Distribute the common factor z̄: F = x z̄ + y z̄ Expand each term to include all variables (so each product is a minterm): x z̄ = x(y + ȳ) z̄ = x y z̄ + x ȳ z̄ Similarly, expand y z̄: y z̄ = y(x + x̄) z̄ = x y z̄ + x̄ y z̄ Combine the expanded terms and remove duplicates: x y z̄ + x ȳ z̄ + x̄ y z̄ Final sum-of-products (minterm) form: F(x,y,z) = x y z̄ + x ȳ z̄ + x̄ y z̄

Answer

A. $\bar x \bar yz + xy\bar z + \bar xy\bar z$

Answer

B. $xyz + xy\bar z + x \bar y \bar z$

Answer

C. $x\bar y \bar z + \bar x \bar y \bar z + xy \bar z$

Answer

D. $xy \bar z + x \bar y \bar z + \bar xy \bar z$

The sum of products expansion for the function \(F(x, y, z) = (x + y)\bar z\)…