Question

(A ∩ B) ∪ (C ∩ D) = (A ∩ D) ∪ (C ∩ B)

help prove the following statement?

Answer 1

did you try to distribute

Answer 2

Distributive laws
$$\Large {
A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\\\
A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\
}$$

Answer 3

yeah, it gives me (A ∪ C) ∩ (A ∪ D) ∩ (B ∪ C) ∩ (B ∪ D) . After I could end up with
(A) ∩ ( D) ∩ ( C) ∩ (B ) and group them, but im still missing the union symbol :/

Answer 4

forget what I just said, use inference rule! thank you