Boolean Operations — Evaluate the statement: The OR function corresponds to Boolean multiplication and the AND function corresponds to Boolean addition.
Digital Electronics
Boolean Algebra and Logic Simplification
Difficulty: Easy
Choose an option
-
ACorrect
-
BIncorrect
-
CTrue only in arithmetic algebra
-
DDepends on representation
Answer
Correct Answer: Incorrect
Explanation
Introduction: In Boolean algebra, operators map to addition and multiplication analogs, but not in the same way as everyday intuition might suggest. This question checks whether you remember which logic operation maps to which algebraic symbol.Given Data / Assumptions:
- Standard Boolean notation is used
- Symbol + denotes OR, and juxtaposition or * denotes AND
Concept / Approach: By convention, OR corresponds to addition (+) and AND corresponds to multiplication (*). The statement reverses this mapping, so it is incorrect.Step-by-Step Solution:
Step 1: Recall identities: A + 0 = A (OR identity) parallels addition identity.Step 2: Recall identities: A * 1 = A (AND identity) parallels multiplication identity.Step 3: Therefore, OR maps to + and AND maps to *; the prompt is reversed.Verification / Alternative check:
Truth tables and algebraic properties (commutativity, associativity, distributivity) align with these mappings.Why Other Options Are Wrong:
Correct: Contradicts standard Boolean convention.True only in arithmetic algebra: Boolean algebra is distinct; the mapping is definitional there.Depends on representation: Mainstream Boolean notation is standardized on these mappings.Common Pitfalls:
Confusing symbolic similarities when switching between integer arithmetic and Boolean algebra.Assuming OR must be multiplication because it can increase value; not applicable in Boolean domain.Final Answer:
Incorrect