Question

A, B, C are three sets, then prove that (A intersection B) X C = (A X C) intersection (B X C)



provide with relevant answer.... ​

Answer 1

Step-by-step explanation:

What I know:

-I need to prove the sets are equal, that is, prove the LH side is a subset of the RH side, and vice versa.

-A×(B∩C) is the set of all ordered pairs with first entry an element of A, and second entry an element of (B∩C).

-(A×B) is the set of all ordered pairs with first entry an element of A, and second entry an element of B.

-(A×C) is the set of all ordered pairs with first entry an element of A, and second entry an element of B.

So (A×B)∩(A×C) is the set of ordered pairs that are both in (A×B) and (A×C).

How can I link these concepts together? I don't need a complete solution; getting started is the hardest part