Prove A union B = B union A A intersection B intersection C = B intersection A intersection C De Morgan law 1 and 2

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(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]

For any two setsA and B prove that

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

(Commultative laws) For any two sets a and B, prove that:
$I . A \cup B = B \cup A$ [Commutative law for union of sets]

$I I . A \cap B = B \cap A$ [Commutative law for intersection of sets]

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