# Boolean algebra prrof question

• hallerman
In summary, the goal is to prove the expression X'Y' + Y'Z + XZ + XY + Z'Y = X'Y' + XZ + YZ' using the laws of Boolean algebra. The two sides are almost the same except for two extra terms on the left, XY and Y'Z. The solution involves breaking up Y'Z as Y'ZX+Y'ZX' and finding other terms on the left that subsume those.

## Homework Statement

Prove the following expression using Boolean algebra:

1. X'Y' + Y'Z + XZ + XY + Z'Y = X'Y' + XZ + YZ'

## Homework Equations

Laws of Boolean algebra

## The Attempt at a Solution

I tried to take Y common but failed. I did the same with X and Z, but the method did not work. Any hints, please?

The two sides are the same except for two extra terms on the left, XY and Y'Z. So you need to show that those two are subsumed by the others. E.g. For Y'Z, you can break it up as Y'ZX+Y'ZX'. Can you find other terms on the left which subsume those?

1 person
Thanks, I got it.

## 1. What is Boolean algebra and how is it used?

Boolean algebra is a mathematical system used for logical operations and comparisons. It is used in computer science and electronics to analyze and simplify logical statements and circuits.

## 2. What is a Boolean proof and how is it constructed?

A Boolean proof is a step-by-step logical argument that uses the laws and rules of Boolean algebra to demonstrate the validity of a statement or equation. It is constructed by breaking down the statement into smaller, simpler parts and applying the laws of Boolean algebra to manipulate and simplify these parts.

## 3. What are the basic laws of Boolean algebra?

The basic laws of Boolean algebra include the commutative law, associative law, distributive law, identity law, and complementation law. These laws govern how logical operations and comparisons can be performed on Boolean values.

## 4. How do you know if a Boolean proof is correct?

A Boolean proof is correct if it follows the rules and laws of Boolean algebra and if each step can be logically justified. This means that each step must be a valid application of a law or rule of Boolean algebra, and the final statement must be equivalent to the original statement.

## 5. Can Boolean algebra be applied to real-world situations?

Yes, Boolean algebra can be applied to real-world situations in fields such as computer science, electronics, and mathematics. It is used to analyze and simplify logical statements and circuits, and it can also be used to model and solve problems in other areas such as economics and game theory.