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SETS

UNIVERSAL SET

Updated May 8, 2023

When working with sets, a reference superset that contains all the sets and their subsets in context (i.e. the sets which are currently under consideration) is…

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SETS

Partitions

Updated May 8, 2023

Partitioning of a set is distributing the member elements of a set among a group of non-empty subsets in such a way that each member lies…

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SETS

Disjoint Sets

Updated May 8, 2023

Two sets A and B are called disjoint when they have no element in common (except the empty set ∅ }.

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SETS

Power Set

Updated May 8, 2023

The set of all possible subsets of a set S is called the power set of S, written as P(S). Examples ⇒ The power set of…

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SETS

Proper Subset

Updated May 8, 2023

If A is a subset of B but A ≠ B, then A is called the proper subset of B, and B is called the proper superset of A. This relationship…

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SETS

Subset

Updated May 8, 2023

If there are two sets A & B such that every element of A is also in B, then A is called a subset of B. In other words, A…

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Equivalent Sets

Updated May 8, 2023

Two sets A and B are said to be equivalent(≡) if each element of A is also an element of B and each element of B is…

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SETS

Equal Sets

Updated May 8, 2023

Two sets A and B are said to be equal(=) if they have the same elements. The elements may not be in the same order. If an…

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SETS

Finite Set

Updated May 8, 2023

A set that has a definite number of elements is called a finite set else it is called an Infinite set. ⇒ A null set is a finite set. ⇒ For…

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Singleton Set

Updated May 8, 2023

A set that has exactly one member is called a singleton set. { 1 } , { ‘a’ } , { x3 | x ∈ N…

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SETS

Empty Set

Updated May 8, 2023

A set that does not have any members is called an empty set. ⇒ Such sets are represented as {} or using the symbol ∅ (derived from Φ) which has been explicitly developed to…

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SETS

Cardinality of Sets

Updated May 8, 2023

The number of elements in a set is called cardinality. The cardinality of a set A is generally represented by |A| or n(A) meaning the number of elements in set…

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