For each of the following logic expressions, find all of the static hazards in the corresponding two-level AND-OR or OR-AND circuit, and design a hazard-free circuit that realizes the same logic function.
(a) F = W ⋅ X + Wʹ ⋅ Yʹ
(b) F = W ⋅ Xʹ ⋅ Yʹ + X ⋅ Yʹ ⋅ Z + X ⋅ Y
(c) F = W ⋅ Y + Wʹ ⋅ Zʹ + X ⋅ Yʹ ⋅ Z
(d) F = Wʹ ⋅ Xʹ + Yʹ ⋅ Z + Wʹ ⋅ X ⋅ Y ⋅ Z + W ⋅ X ⋅ Y ⋅ Zʹ
(e) F = (Wʹ + X + Yʹ) ⋅ (Xʹ + Zʹ)
(f) F = (W + Yʹ + Zʹ) ⋅ (Wʹ + Xʹ + Zʹ) ⋅ (Xʹ + Y + Z)
(g) F = (W + Y + Zʹ) ⋅ (W + Xʹ + Y + Z) ⋅ (Xʹ + Yʹ) ⋅ (X + Z)
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