Absorption laws
The absorption laws are a set of two fundamental laws in Boolean algebra that describe the behavior of logical operations involving the “AND” and “OR” operators
The absorption laws are a set of two fundamental laws in Boolean algebra that describe the behavior of logical operations involving the “AND” and “OR” operators. These laws focus on the concept of absorption, which means that when we combine a value with its corresponding identity element under a specific operation, the result equals the value itself.
The first absorption law states that for any two variables A and B:
A + (A · B) = A
This law states that if we take the logical OR (represented by the “+” symbol) of a variable A with the logical AND (represented by the “·” symbol) of A and B, the result will always be A. This can be explained by considering the fact that if A is true, then A · B will also be true. Therefore, taking the logical OR of A with the true value of A · B will result in A, as any value OR’ed with true will always be true.
The second absorption law states that for any two variables A and B:
A · (A + B) = A
This law states that if we take the logical AND of a variable A with the logical OR of A and B, the result will always be A. This can be understood by considering that if A is true, then A + B will also be true. Therefore, taking the logical AND of A with the true value of A + B will result in A, as any value AND’ed with true will always be the original value.
These absorption laws are useful in simplifying logical expressions and reducing the number of terms in a Boolean equation. They help in identifying redundant terms and reducing complexity in Boolean algebra operations.
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