Question

Помогите упростить: (B and not C) or C and (A ↔ B)

Answer 1

Решение внутри
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Answer 2

Simplifying the Expression: (B and not C) or C and (A ↔ B)

To simplify the given expression (B and not C) or C and (A ↔ B), let's break it down step by step.

1. Start by simplifying the expression (A ↔ B). The biconditional operator ↔ is equivalent to the logical expression ((A and B) or (not A and not B)). So, we can rewrite the expression as: (B and not C) or C and ((A and B) or (not A and not B))

2. Next, let's simplify the expression (B and not C). This expression represents the logical AND operation between B and the negation of C. The result will be true only if B is true and C is false. So, we can rewrite the expression as: (B and not C) = B and (not C)

3. Similarly, let's simplify the expression C and ((A and B) or (not A and not B)). This expression represents the logical AND operation between C and the expression ((A and B) or (not A and not B)). The result will be true only if C is true and either (A and B) or (not A and not B) is true. So, we can rewrite the expression as: C and ((A and B) or (not A and not B)) = C and (A and B) or C and (not A and not B)

4. Now, let's combine the simplified expressions from steps 2 and 3. We have: (B and not C) or C and ((A and B) or (not A and not B)) = (B and (not C)) or (C and (A and B)) or (C and (not A and not B))

5. Finally, let's simplify the expression further. We can distribute the OR operator over the three terms: (B and (not C)) or (C and (A and B)) or (C and (not A and not B)) = (B and not C) or (C and A and B) or (C and not A and not B)

So, the simplified expression for (B and not C) or C and (A ↔ B) is (B and not C) or (C and A and B) or (C and not A and not B).

Please note that the above simplification assumes that A, B, and C are boolean variables that can take either true or false values.