Lilia said:Homework Statement
i'm viewing an example written in class. it looks like this:
f(x1, x2, x3, x4) = [(not x1) * x2 * x4] ∨ [x2 * x3 * x4]
what should be function after applying absorption law?
Homework Equations
i know how another option called "gluing" works:
[x1 * x2 * x3] ∨ [(not x1) * x2 * x3] = x2 * x3
The Attempt at a Solution
our teacher wrote f(x1, x2, x3, x4) = x2 * x3 * x4 but I'm having a hard time to understand why
Are you sure you typed the question right? The form of your equation doesn't seem to match the OR form of the Absorptive Law...
- Absorptive Law – This law enables a reduction in a complicated expression to a simpler one by absorbing like terms.
- A + (A.B) = A (OR Absorption Law)
- A(A + B) = A (AND Absorption Law)
The Boolean algebra absorption law is a rule that states that when a Boolean expression is ANDed with one of its terms, the result is equal to the term. This means that if you have an expression like A AND (A OR B), the result is simply A. This is known as the first absorption law.
The second absorption law states that when a Boolean expression is ORed with one of its terms, the result is equal to the term. This means that if you have an expression like A OR (A AND B), the result is simply A. This is known as the second absorption law.
The absorption law is used in simplifying Boolean expressions by reducing them to their simplest form. By applying the absorption law, you can eliminate redundant terms and reduce the complexity of the expression.
The absorption law and the distributive law are complementary laws in Boolean algebra. While the absorption law states that a term can be absorbed by an AND or OR operation with itself, the distributive law states that a term can be distributed across an AND or OR operation over a sum or product of terms.
Yes, the absorption law can be applied to more than two terms in a Boolean expression. For example, in the expression A AND (B OR C OR D), the absorption law can be applied repeatedly to eliminate all the redundant terms and simplify the expression to just A.