Which of the following is the canonical SOP (Sum of Products) form equivalent…
2026
Which of the following is the canonical SOP (Sum of Products) form equivalent to the following canonical POS (Product of Sums) form as per Boolean Algebra?
(U′ + V) · (U + V′)
Answer: C. U′·V′ + U·V — Given POS expression: (U′ + V)(U + V′). Expanding by the distributive law: (U′ + V)(U + V′) = U′U + U′V′ + VU + VV′ Using the complement law, U′U = 0 and VV′…
- A.
U′·V + U·V′
- B.
U′·V′ + U′·V
- C.
U′·V′ + U·V
- D.
U·V′ + U·V
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Correct answer: C
Given POS expression: (U′ + V)(U + V′).
Expanding by the distributive law:
(U′ + V)(U + V′) = U′U + U′V′ + VU + VV′
Using the complement law, U′U = 0 and VV′ = 0.
So the expression becomes U′V′ + UV.
Thus, the equivalent canonical SOP form is U′·V′ + U·V, which is the XNOR/equivalence function. Therefore, Option C is correct.