Question

Explain the rule of association in Boolean Algebra.

Hint:

Think of it like regular addition: (2+3)+4 is the same as 2+(3+4). The associative law says the same principle applies to Boolean AND and OR operations.

Answer 1

The Associative Law in Boolean algebra states that the grouping of variables in an AND or an OR operation does not affect the outcome. For three variables A, B, and C, the law is defined by two rules:

Associative Law of Addition (OR): \( (A + B) + C = A + (B + C) \)
Associative Law of Multiplication (AND): \( (A \cdot B) \cdot C = A \cdot (B \cdot C) \)
This rule allows us to remove the parentheses when combining three or more variables with the same operator.