Consider F = (X + Y + Z)(X′ + Y)(Y′ + Z). Which of the following are equivalent to F′? A. (X′ + Y′ + Z′)(X + Y′)(Y + Z′) B. XY′ + Z′ C. (X + Z′)(Y′ + Z′) D. XY′ + YZ′ + X′Y′Z′

1. AA, B and C Only
2. BB, C and D Only
3. CA, C and D Only
4. DA, B and D Only

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Correct answer: B. B, C and D Only

Explanation

By De Morgan, F′ = X′Y′Z′ + XY′ + YZ′ (D). This simplifies: YZ′ + X′Y′Z′ + XY′Z′ = Z′, so F′ = XY′ + Z′ (B). Expanding (X + Z′)(Y′ + Z′) also gives XY′ + Z′ (C). Expression A is not equal.