For any sets A, B, C, D, prove that (A×B) ∩ (C×D) = (A∩C) × ( B∩D) Question For any sets A, B, C, D, prove that (A×B) ∩ (C×D) = (A∩C) × ( B∩D) in progress 0 Math Ariana 2 months 2021-10-04T21:57:16+00:00 2021-10-04T21:57:16+00:00 1 Answer 0 views 0

## Answers ( )

Answer:Show that (A×B)∩(C×D)⊆(A∩C)×(B∩D) first, and then show the other inclusion ⊇.

For ⊆: Let z=(x,y)∈(A×B)∩(C×D). That means (x,y)∈A×B and (x,y)∈C×D. Now finish it and conclude that z=(x,y)∈(A∩C)×(B∩D).

For ⊇: Let z=(x,y)∈(A∩C)×(B∩D). That means x∈A∩C and y∈B∩D. Now conclude.

Step-by-step explanation:please follow me and add me to your brain list