# A function πΉ(π΄, π΅, πΆ) defined by three Boolean variables A, B and C when expressed as sum of products is given by

Q. A function πΉ(π΄, π΅, πΆ) defined by three Boolean variables A, B and C when expressed as sum of products is given by

πΉ = π΄Μ β π΅Μ β πΆΜ + π΄Μ β π΅ β πΆΜ + π΄ β π΅Μ β πΆΜ

where, π΄Μ, π΅Μ, and πΆΜ are the complements of the respective variables. The product of sums (POS) form of the function F is

(A) πΉ = (π΄ + π΅ + πΆ) β (π΄ + π΅Μ + πΆ) β (π΄Μ + π΅ + πΆ)

(B) πΉ = (π΄Μ + π΅Μ + πΆΜ) β (π΄Μ + π΅ + πΆΜ) β (π΄ + π΅Μ + πΆΜ)

(C) πΉ = (π΄ + π΅ + πΆΜ) β (π΄ + π΅Μ + πΆΜ) β (π΄Μ + π΅ + πΆΜ) β (π΄Μ + π΅Μ + πΆ) β (π΄Μ + π΅Μ + πΆΜ)

(D) πΉ = (π΄Μ + π΅Μ + πΆ) β (π΄Μ + π΅ + πΆ) β (π΄ + π΅Μ + πΆ) β (π΄ + π΅ + πΆΜ) β (π΄ + π΅ + πΆ)

Ans: F = (A + B + CΜ) . (A + BΜ + CΜ) . (AΜ + B + CΜ) . (AΜ + BΜ + C) . (AΜ + BΜ + CΜ)

Sol:

F = AΜ.BΜ.CΜ + AΜ.B.CΜ + A.BΜ.CΜ

In terms of minterms, this can be represented as:

F = βmΒ (0, 2, 4)

The equivalent maxterm will contain the terms not present in the minterm representation, i.e.

F =Β βm (0, 2, 4) = Ο(1, 3, 5, 6, 7) = M1. M3. M5. M6. M7

β (A + B + CΜ) (A + BΜ + CΜ) (AΜ + B + CΜ) (AΜ + BΜ + C) (AΜ + BΜ + CΜ)

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