How do I simplify this boolean function using the rules of boolean algebra?

In summary, the conversation revolves around simplifying a boolean function and proving its equality using the rules of boolean algebra. The specific problem being discussed is changing the left hand side of the equation CA + CB + B'A to the right hand side, CB + B'A. The person speaking is stuck at this step and is looking for help in understanding the algebraic steps to prove the equality. They also mention that according to a truth table, the two expressions are equal, but they are unable to prove it algebraically.
  • #1
Ownaginatious
38
0
Okay, so I'm stuck at a step of a much bigger problem where I have to simplify a boolean function.

Homework Statement



Here is where I'm stuck, I have to change the left hand side to the right hand side. How do I prove this with the rules of boolean algebra?

CA + CB + B'A = CB + B'A

Homework Equations



0199541454.boolean-algebra.1.jpg


The Attempt at a Solution



The above is as far as I've gotten (as I said, this was taken from a bigger problem).

Can someone please show me the steps that will change the left hand side of the equation to the right? According to truth tables, they are infact equal.
 
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  • #2
This appears wrong as the expression you wrote implies A+B=B, which is not true for a complete truth table.
 
  • #3
Well, according to this truth table, it's right:

http://img170.imageshack.us/img170/3023/truth.png

I can't figure out how to prove this algebraically though.
 
Last edited by a moderator:

FAQ: How do I simplify this boolean function using the rules of boolean algebra?

What is Boolean algebra?

Boolean algebra is a branch of mathematics and logic that deals with binary variables and logical operations. It is used to simplify and analyze logical statements and circuits.

What are the basic operations in Boolean algebra?

The basic operations in Boolean algebra are AND, OR, and NOT. These operations allow for the manipulation and simplification of logical statements.

How do I solve a Boolean algebra problem?

To solve a Boolean algebra problem, you can use truth tables, laws and theorems of Boolean algebra, and logic gates. It is important to simplify the expression by applying the laws and theorems before using a truth table or logic gate.

What are some applications of Boolean algebra?

Boolean algebra has many practical applications, including in computer science, digital electronics, and database searching. It is also used in the design and analysis of control systems and mathematical proofs.

Are there any laws or properties in Boolean algebra?

Yes, there are several laws and properties in Boolean algebra, including the commutative, associative, and distributive laws, as well as the identities and complement laws. These laws and properties help simplify and solve Boolean algebra problems.

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