Convert the Boolean function F(A, B, C) = Π(0, 2, 4, 5, 7) to its simplified…
2025
Convert the Boolean function F(A, B, C) = Π(0, 2, 4, 5, 7) to its simplified POS form.
- A.
A + B + C
- B.
A.B + B′C
- C.
C.ABC′
- D.
(A + B)(A + C)(B + C)
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Correct answer: D
Step 1: The given Boolean function is F(A, B, C) = Π(0, 2, 4, 5, 7), which means the maxterms are 0, 2, 4, 5, and 7. Step 2: The minterms not included are 1, 3, and 6. So, the function in SOP form is F(A, B, C) = Σ(1, 3, 6). Step 3: To convert to POS form, we use the maxterms directly. The POS form is the product of sums corresponding to the maxterms. Step 4: Using a K-map or Boolean algebra, the simplified POS form is (A + B)(A + C)(B + C).