Thread: Cross Products and Set Unions Proof

I'm hoping this is the right category, since it's set theory. If it's not I'll move it if someone knows a better place for these questions

Prove that A X (B₁U B₂) = (A X B₁) U (A X B₂)

I am actually stuck on the B₁ B₂ in this problem. It's some notation aspect that is keeping me from understanding what the problem is asking for. Are B₁ and B₂ separate sets?

Originally Posted by renolovexoxo

Are B₁ and B₂ separate sets?

Yes, B₁ and B₂ are arbitrary sets. The problem is asking to prove that A x (B U C) = (A x B) U (A x C) for arbitrary sets A, B, C.

Originally Posted by renolovexoxo

I'm hoping this is the right category, since it's set theory. If it's not I'll move it if someone knows a better place for these questions

Prove that A X (B₁U B₂) = (A X B₁) U (A X B₂)