Solution

The correct answer is A' + BC'

Key PointsA Karnaugh Map (K-map) is a visual method used for simplifying Boolean expressions. It provides a straightforward way to minimize expressions with two, three, four, or more variables. The map is a grid where each cell represents a min-term of the Boolean function. By organizing these min-terms in a specific pattern, it becomes easier to spot opportunities for simplification.

Don't-care terms (denoted as (x)) are used in Boolean functions to indicate that for certain combinations of variables, the output value can be either 0 or 1 without affecting the overall functionality of the circuit or logic. These terms provide flexibility for further simplification and optimization of the Boolean expression.

Solution:

=> (A'B'C' + A'B'C + A'BC + A'BC') + (A'BC' + ABC')

=> A(B'C' + B'C + BC + BC') + BC'(A' + A)

=> A' + BC'

So, the correct answer is A' + BC'