In the set, we need to solve different types of problems. For that, we have to apply

**some rules of the sets**. Previously we have discussed the Set in mathematics and its types.## Some rules of the sets

Rules of the set union, intersection, and minus

A) If A, B, C are the subset of universal set U then-

- A∪A = A (A union B equals A)
- A∩A = A (A intersection B equals to A)
- A∪∅ = A (A union Empty set equals to A)
- A∩U= A (A intersection universal set equals to A)
- A∩∅ = ∅ (A intersection Empty set equals to Empty set)

Proves:

- In A∪A all elements are the union of set A and set A. Without repeating the same element we get set A∪A = A.
- A∩A common elements of A and A will be the element of the set. So, A∩A =A.
- Because ∅ has no element so A∪∅=A.
- Because A is the subset of U so common elements of A and U will be the elements of A.
- Because ∅ has no elements so A and ∅ has no common elements.

B) If A, B are two sets then-

- A∪B = B∪A
- A∩B = B∩A

These two are the

**commutative laws**of sets.C) If A,B,C are 3 sets then-

- A∪(B∪C) = (A∪B)∪C
- A∩(B∩C) = (A∩B)∩C

These two are the

**associative laws**of sets.D) If A, B, C are thee sets then-

- A∪(B∪C) = (A∪B)∩(A∪C)
- A∩(B∩C) = (A∩B)∪(A∩C)

These laws are

**distributive laws**of sets.E)If A, B are the subset of universal set U then

- (A∪B)´ = Aˊ∩ Bˊ
- (A∩B)´ = A´∪ B´

This law is De Morgan's theorem.

So these were

**some rules of the sets**.
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