NULL/ VOID/ EMPTY SET
A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and n (Φ) = 0 as it has no element. For example the set of all real numbers whose square is -1.
SINGLETON SET
A set having only one element is called Singleton Set.
FINITE AND INFINITE SET
A set, which has limited numbers of members, is called as finite set. Otherwise it is known as an in finite set. As like, the set of all weeks in a year is a finite set while, the set of all real number is an infinite set.
UNION OF SETS
Union of two or more than two sets is the set of all components that related to any of these sets.
INTERSECTION OF SETS
It is the set of all the members, which are usual to all the sets. The symbol shown for intersection of sets is
'∩' i.e. A ∩ B = {x: xÎA and xÎ B}
Problem: If A = {1, 2, 3, 4} and B = {2, 4, 5, 6} and C = {1, 2, 6, 8}, then A∩B ∩ C = {2}
DIFFERENCE OF SETS
The difference of set A to B shown as A- B is the set of those members that are in the set A but not in the set B i.e. A - B = {x: xÎA and x ÎB}
Equally B -A = {x: xÎB and xÎ A}
In usual A-B ? B-A
Problem: If A = {a, b, c, d} and B = {b, c, e, f} then A-B = {a, d} and B-A = {e, f}.
Symmetric Difference of Two Sets:
For two sets B and A, symmetric difference of B and A is provided by (A - B) È (B - A) and is shown by A D B.
SUBSET OF A SET
A set A is called be a subset of the set B if each and every element of the set A is also the member of the set B. The symbol taken is 'Í'
Every set is a subset of its own set. Also a void set is a part of any set. If there is at least one member in B which does not related to the set A, then A is a proper subset of set B and is shown as A Ì B. e.g If A = {a, b, c, d} and B = {b, c, d}. Then BÌA or similarly AÉB (i.e A is a super set of B). Total number of group or subsets of a finite set containing n members is 2n.
DISJOINT SETS
If two sets A and B have no similar members i.e. if no component of A is in B and no element of B is in A, then A and B are known as be Disjoint Sets. Therefore for Disjoint Sets A and B n (A ∩ B) = 0.