Let f(w, x, y, z) = ∑(0, 4, 5, 7, 8, 9, 13, 15). Which of the following…

Given function f: Σ(0,4,5,7,8,9,13,15).

Verify each candidate expression by listing the minterms it produces.

• x'y'z' + w'xy' + wy'z + xz covers minterms {0, 8} from x'y'z', {4, 5} from w'xy', {9, 13} from wy'z, and {5, 7, 13, 15} from xz. Union = {0,4,5,7,8,9,13,15} which matches f.

• w'y'z' + wx'y' + xz covers minterms {0, 4} from w'y'z', {8, 9} from wx'y', and {5, 7, 13, 15} from xz. Union = {0,4,5,7,8,9,13,15} which matches f.

• w'y'z' + wx'y' + xyz + xy'z covers minterms {0,4} from w'y'z', {8,9} from wx'y', {7,15} from xyz, and {5,13} from xy'z. Union = {0,4,5,7,8,9,13,15} which matches f.

• x'y'z' + wx'y' + w'y covers minterms {0,8} from x'y'z', {8,9} from wx'y', and {2,3,6,7} from w'y. Union = {0,2,3,6,7,8,9} which does NOT equal f. It misses 4,5,13,15 and includes extra minterms 2,3,6.

Counterexample: minterm 2 (w=0, x=0, y=1, z=0) makes x'y'z' + wx'y' + w'y true (via w'y) but f is 0 at minterm 2, so the expressions are not equivalent.

Conclusion: The only expression that is NOT equivalent to f is x'y'z' + wx'y' + w'y. The other three expressions produce exactly the minterms of f.