Question

F = W ⋅ X ⋅ Y ⋅ Z ⋅ (W ⋅ X ⋅ Y ⋅ Z′ + W ⋅ X′ ⋅ Y ⋅ Z + W′ ⋅ X ⋅ Y ⋅ Z + W ⋅ X ⋅ Y′ ⋅ Z)

With switching algebra, what would it be simplified

Answer 1

F = W ⋅ X ⋅ Y ⋅ Z ⋅ (W ⋅ X ⋅ Y ⋅ Z′ + W ⋅ X′ ⋅ Y ⋅ Z + W′ ⋅ X ⋅ Y ⋅ Z + W ⋅ X ⋅ Y′ ⋅ Z)
= (W ⋅ X ⋅ Y ⋅ Z ⋅ W ⋅ X ⋅ Y ⋅ Z′ + W ⋅ X ⋅ Y ⋅ Z ⋅ W ⋅ X′ ⋅ Y ⋅ Z + W ⋅ X ⋅ Y ⋅ Z ⋅ W′ ⋅ X ⋅ Y ⋅ Z + W ⋅ X ⋅ Y ⋅ Z ⋅ W ⋅ X ⋅ Y′ ⋅ Z)
= (0 + 0 + 0 + 0)   ->  (because W.W' = 0, X.X' = 0, Y.Y' = 0, Z.Z' = 0)
= 0

so, F = 0