A Level Computer Science OCR Practice Exam

In boolean logic, what does the expression B^AvB^C simplify to?

1. B(AvC)

2. A(BvC)

3. C(BvA)

4. A^B^C

The correct answer is: B(AvC)

The expression \( B \land A \lor B \land C \) can be simplified to \( B \land (A \lor C) \). This follows from the distributive property in Boolean algebra, which states that \( X \land (Y \lor Z) \) is equivalent to \( (X \land Y) \lor (X \land Z) \). In this case, you can factor out \( B \) from both terms \( B \land A \) and \( B \land C \), leading to the expression \( B \land (A \lor C) \). This demonstrates that the presence of \( B \) in both parts of the expression allows it to be factored out, making the expression more compact and revealing the relationship between \( A \) and \( C \). The simplification to \( B(A \lor C) \) effectively captures the logical structure of the original expression, illustrating how certain conditions (involving \( A \) and \( C \)) depend on another condition \( B \).