(A + B) + C is the same as?

(A + B) + C is the same as?

• A. A+(B+C)
• B. (A+B)+C
• C. A+(B·C)
• D. A·(B+C)

Answer: (A)

This question tests the associative property of the OR operation in boolean logic. OR is associative, so grouping doesn’t matter: (A OR B) OR C equals A OR (B OR C). Therefore, (A + B) + C is the same as A + (B + C). This is effectively A OR B OR C, regardless of how you parenthesize the expression. The other forms mix OR and AND in ways that change the result in general. For example, A OR (B AND C) can differ from A OR B OR C, and A AND (B OR C) can also yield a different outcome than A OR B OR C. A quick check with simple values shows the difference: if A=0, B=0, C=1, then (A+B)+C = 1, but A+(B·C) = 0 and A·(B+C) = 0, proving these aren’t equivalent to A OR B OR C.

This question tests the associative property of the OR operation in boolean logic. OR is associative, so grouping doesn’t matter: (A OR B) OR C equals A OR (B OR C). Therefore, (A + B) + C is the same as A + (B + C). This is effectively A OR B OR C, regardless of how you parenthesize the expression.

The other forms mix OR and AND in ways that change the result in general. For example, A OR (B AND C) can differ from A OR B OR C, and A AND (B OR C) can also yield a different outcome than A OR B OR C. A quick check with simple values shows the difference: if A=0, B=0, C=1, then (A+B)+C = 1, but A+(B·C) = 0 and A·(B+C) = 0, proving these aren’t equivalent to A OR B OR C.