(A union B)' = A' union B ' prove

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If A is a subset of B , then prove that A union B is B .

For any two setsA and B prove that

A intersection (A' union B ) = A intersection B

(Distributive laws) For any three sets A, B, C prove that:

I. $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
[Distirbutive law of union over intersection]

II. $A \cap [(B \cup C)] = (A \cap B) \cup (A \cap C)$
[Distributive law of intersection over union]

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