Question

For any sets A, B, C, D, prove that

(A×B) ∩ (C×D) = (A∩C) × ( B∩D) ​

Answer 1

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:

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