Prove an Identity in Boolean Algebra: Help Needed!

In summary, the conversation discusses the challenge of proving a given identity, (A + C).(notA + B) = A.B + notA.C, and the use of the distribution rule in solving it. The person seeking help has already started with the left-hand side, but has encountered an extra term, B.C. They are looking for guidance on how to proceed and are given a hint to multiply something by either (A + notA) or (C + notC).
  • #1
jksdvb8
1
0
May seem easy, I can't do it though...

I'm given an identity to prove:-

(A + C).(notA + B) = A.B + notA.C

I've started with LHS, multiplied out and ended up with an extra B.C. I think this has something to do with the distribution rule but I don't know how to work it through

Any help greatly appreciated

JK
 
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  • #2
welcome to pf!

hi jksdvb8! welcome to pf! :smile:
jksdvb8 said:
I've started with LHS, multiplied out and ended up with an extra B.C.

so you need to prove that B.C is contained in A.B + notA.C

hint: multiply something by either (A + notA) or (C + notC) :wink:
 

1. What is Boolean Algebra?

Boolean Algebra is a branch of mathematics and a type of algebraic structure that deals with binary variables and logical operations. It is used to analyze and simplify logical expressions and circuits, and to prove identities that describe relationships between these expressions.

2. How do you prove an identity in Boolean Algebra?

To prove an identity in Boolean Algebra, you need to use the basic laws and theorems of the algebra, such as the commutative, associative, distributive, and De Morgan's laws. You can also use truth tables, algebraic manipulations, and logical equivalences to show that both sides of the identity are equivalent.

3. What are the basic laws of Boolean Algebra?

The basic laws of Boolean Algebra are the commutative, associative, and distributive laws, as well as the identity and complement laws. These laws govern the manipulation of logical expressions and help simplify them.

4. What are some common identities used in Boolean Algebra?

Some common identities used in Boolean Algebra include the double negation law, the idempotent law, the absorption law, and the complementarity law. These identities can be used to simplify and prove other more complex identities.

5. What are some tips for proving identities in Boolean Algebra?

Some tips for proving identities in Boolean Algebra include starting with the simpler side, using truth tables to verify the identity, being organized and methodical in your approach, and double-checking your work. It is also helpful to have a good understanding of the basic laws and theorems of the algebra.

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