Prove Absorption Law: A U (A and B) = A

In summary, the conversation is about proving the absorption law in Boolean Algebra, specifically A U (A and B) = A. The person is struggling with proving the right hand as a subset of the left hand and is considering using the concept of partition. They are asking for assistance in completing the proof.
  • #1
jwxie
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Homework Statement



Prove the absorption law A U (A and B) = A

Homework Equations



The Attempt at a Solution



I need to prove the sets are equal.

I don't know how to prove the right hand as a subset of the left hand.
For left hand as subset of right hand, it's pretty simple (we can define a new called G holding x in A and in B), and G is subset of A, then G U A is A (definition of subset and Union).

But how do I prove the right hand?
I started writing "There exists a set A..." and I thought about using partition, but then I couldn't go on anymore. If I say there exists an arbitrary set B, and x in A and B, then I am again writing the first proof.

Can someone please help me? Thanks.
 
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  • #2
Is this set theory or Boolean Algebra? Boolean Algebra I think.
 

FAQ: Prove Absorption Law: A U (A and B) = A

What is the Absorption Law?

The Absorption Law is a fundamental rule in Boolean algebra that states that the union of a set with the intersection of that set with another set is equal to the original set. In other words, A union (A intersection B) is equal to A.

Why is the Absorption Law important?

The Absorption Law is important because it allows us to simplify complex Boolean expressions and make them more manageable. It also has many practical applications in computer science, logic circuits, and database queries.

How do you prove the Absorption Law?

To prove the Absorption Law, we can use a truth table or apply the distributive property. We can also use Venn diagrams to visually demonstrate the concept.

What are the applications of the Absorption Law?

The Absorption Law has many applications in computer science, logic circuits, and database queries. It is also used in simplifying mathematical expressions and solving equations.

Are there any exceptions to the Absorption Law?

No, the Absorption Law is a fundamental rule in Boolean algebra and is always true. There are no exceptions to this law.

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