## More types of sets: Disjoint sets, Subset and Universal set

Disjoint sets:

Two or more sets are said to be disjoint if they have no common elements.

Disjoint-sets are also known as non overlapping sets. For example:

A={2,4,6,8} and B={1,3,5,7}. Here A and B have no common element. So A and B are disjoint-sets.

Overlapping-sets:

Two-sets are said to be overlapping-sets if they contain at least one element in common.

For example:

A={2,4,6,8}

B={3,6,9}here A and B have one common element that is 6. So A and B are overlapping sets.

Universal set:

A universal set is a set of all possible elements under given definition. It is usually denoted by U or ξ .

Subset:

If A and B are two given sets, and if all the elements of A are also elements of B, then A is a subset of B.

• If all elements of set B are also element of A then B is a subset of A.
• In other words, A is a subset of B if and only if every element of A is in B
• The symbol to denote subset is .
• For example, If A is a subset of B, then it is denoted by A⊆B.

Type of subset:

Proper subset:

A is a proper subset of B if and only if every element of A must also be the element of the set B, and also there exists at least one element in B which is not an element of A

Note:

• The symbol to denote proper subset is .
• Every set is a subset of itself. A⊂ A.
• Empty set or null set or ∅ is the subset of every set
• When we say that A is a subset of B we denote by A⊆B.
• When we say that A is a proper subset of B then we denote it as A⊂B.

Super set:

Whenever A is a subset of B, then B is the super set of A. It is expressed as B⊇A.

Examples:

U={x:x is a natural number; 1‹x‹10}

A={x:x is a even natural number; x‹10}

B={x:x∈N;x=3N;x≤9}

C={2,4,6} 