Which of the following options is equivalent to the Boolean expression…

Concept: in a sum-of-products expression, any literal that appears in every product term can be pulled outside the sum by the distributive law. What remains inside is then collapsed by two identities of Boolean algebra: the complement law X + X' = 1, and the identity law Y · 1 = Y.

Applying this to A'C + A'BC' + A'B'C':

1. The literal A' appears in all three product terms, so factor it out: A'C + A'BC' + A'B'C' = A'(C + BC' + B'C').

2. Inside the bracket, C' is common to the last two terms: C + BC' + B'C' = C + C'(B + B').

3. By the complement law, B + B' = 1, so the bracket becomes C + C' · 1 = C + C'.

4. By the complement law again, C + C' = 1, so the whole bracket equals 1.

5. By the identity law, A' · 1 = A'.

Cross-check on the truth table: every product term contains A', so the expression is 0 on all four rows where A = 1. For A = 0 the three terms cover C = 1 (from A'C), B = 1 with C = 0 (from A'BC'), and B = 0 with C = 0 (from A'B'C') — that is all four rows where A = 0. So the expression is 1 exactly when A = 0.

Result: the expression simplifies to A'.