(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am to prove that AU(AΠB)=AΠ(AUB)=A where Π means intersection

2. Relevant equations

3. The attempt at a solution

LHS xЄA or, xЄ(AΠB)

=> xЄA or, (xЄA and xЄB)

=> (xЄA or, xЄA) and (xЄA or,xЄB)

=>xЄA and xЄ(AUB).............................This is precisely AΠ(AUB)

x is an element of both A and (AUB),that is what the and operation mean.

Hence xЄA..........................proved from one side.

Now we are to prove that yЄA =>yЄ AU(AΠB)

Since A is a subset of AU(AΠB),it follows that if yЄA,it must be true that yЄ AU(AΠB)

Again,since AU(AΠB)=AΠ(AUB),hence yЄ AΠ(AUB) too.

Hence proved.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Please check this problem

**Physics Forums | Science Articles, Homework Help, Discussion**