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Q138 (CISF/2020) Science & Technology › ICT, AI, Cybersecurity & Emerging Tech

Convert F(A, B, C) = (A + B̅) (B + C) into canonical Product of Sum form.

Explanation

To convert the Boolean expression F(A, B, C) = (A + B̅)(B + C) into canonical Product of Sum (POS) form, each sum term (maxterm) must contain all three variables (A, B, and C).

  1. Expand (A + B̅): Add the missing variable C using the identity X + 0 = X and Y · Y̅ = 0.
    (A + B̅ + C · C̅) = (A + B̅ + C)(A + B̅ + C̅)
  2. Expand (B + C): Add the missing variable A.
    (B + C + A · A̅) = (A + B + C)(A̅ + B + C)
  3. Combine all unique terms: F = (A + B + C)(A̅ + B + C)(A + B̅ + C)(A + B̅ + C̅)

Comparing this result with the given options, Option C contains three of these valid maxterms: (A̅ + B + C), (A + B̅ + C̅), and (A + B̅ + C). Other options are incorrect because they include terms like (A̅ + B̅ + C) or (A̅ + B + C̅), which evaluate to 1 for the given function.

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