# Solve Boolean Algebra Homework Problem

• Tokenfreak
ABC + ~ABC, then use distributive propertyIn summary, the conversation discusses using Boolean algebra to show the equality of two expressions. The first expression is given and the solution is provided, while the second expression is given and the student asks for help simplifying it. The expert advises the use of truth tables and provides a hint for simplifying the second expression using the distributive property.
Tokenfreak

## Homework Statement

I am suppose to use Boolean algebra to show that the following expressions are true.

## Homework Equations

w'z' + w'xy + wx'z + wxyz = w'z' + xyz + wx'y'z + wyz

## The Attempt at a Solution

I have tried to figure out how to get to that answer above but I am stuck and not sure what to do or if I am even doing it right. Here is what I got so far:

w'(z + xy) + w(x'z +xyz)
w'(z + xy) + wz(x' + xy)
w'(z + x' + y') + wz(x' + x' + y')
w'(z + x' + y') + wz(x' + y')

Thanks!

When a solution is not obvious, consider whether to first draw up truth tables to show that equality holds. If there is an error in the expressions you are given, this will reveal it before you waste a lot of time on an exercise in futility.

You have some errors in your derivation; xy ≠ x'+y' , for example.

Here's a hint: w'xy = w'xy(z+z') = w'xyz + w'xyz'

And yes, truth tables are definitely useful here.

Y=(AB)+(~AC)+(BC)

Z= (AB)+(~AC)

thanks

Help #1: Use truth tables
Help #2: BC = (A+~A)BC

## What is Boolean algebra?

Boolean algebra is a type of algebraic system that deals with logical expressions and operations. It is used to represent and manipulate logical statements, which are either true (represented by 1) or false (represented by 0).

## How is Boolean algebra used in solving homework problems?

Boolean algebra is used to simplify and solve complex logical expressions. It allows us to break down a problem into smaller parts and apply logical operations to arrive at a solution.

## What are the basic operations in Boolean algebra?

The basic operations in Boolean algebra are AND, OR, and NOT. These are represented by the symbols • (dot), + (plus), and ¬ (tilde), respectively. The AND operation evaluates to true only if both operands are true. The OR operation evaluates to true if either or both operands are true. The NOT operation reverses the truth value of an operand.

## How do I solve a Boolean algebra homework problem step by step?

To solve a Boolean algebra homework problem, follow these steps:

1. Identify the given logical expression and write it down using Boolean variables (e.g. A, B, C).
2. Simplify the expression using the basic operations (AND, OR, NOT) and the rules of Boolean algebra (e.g. De Morgan's laws, distributive property).
3. Use truth tables to evaluate the expression and check your work.
4. If the problem involves multiple expressions, combine the simplified expressions using Boolean algebra.
5. Double-check your final answer and make sure it satisfies the given constraints.

## What are some common mistakes to avoid when solving Boolean algebra homework problems?

Some common mistakes to avoid when solving Boolean algebra homework problems are:

• Forgetting to use parentheses to indicate the order of operations.
• Not applying the rules of Boolean algebra correctly (e.g. incorrectly applying De Morgan's laws).
• Using the wrong Boolean variable or operation symbol.
• Not simplifying the expression enough.
• Forgetting to check the final answer against the given constraints.

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