Practice Questions on Set Theory

Set Theory:

The set which does not contain any element is known as an empty set or a null set.
If every point of set A belongs to B then A is contained or included in B & called suset of B. B is called trhe superset of a.This is represented as A ⊂ B or B ⊃ A
Two sets are identical,if they contain exactly same points and is then denoted as A = B.Another way to represent this is A = B if and only if A ⊂ B or B ⊂ A

Operation with Sets:

The union of two sets A and B (A ∪ B) is the set of points which belongs to atlease one of them.
The intersection of two sets A and B (A ∩ B) is the set of points which belongs to both of them.
Sets obey commutative law od union and intersection.
A ∪ B = B ∪ A ; A ∩ B = B ∩ A
Sets obey associative law of union and intersection
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
Sets obey distributive law of union and intersection
(A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)
(A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C)

De Morgan's Law:

(A ∪ B)^c = A^c ∩ B^c
(A ∩ B)^c = A^c ∪ B^c