MATHEMATICS
Resources & Insights

Explore mathematics, the foundational science of numbers, patterns, and logical reasoning. Learn key topics including algebra, geometry, calculus, statistics, and number theory. Ideal for students, educators, and enthusiasts seeking to develop problem-solving skills and apply mathematical concepts in science, technology, finance, and everyday life.

Disjoint Sets

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

Power Set

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 { ‘a’ } is { ∅, {‘a’} }The power set of { 2, 3 } is { ∅, {2}, {3}, {2,3} }The power set of {1, 2, 3 } is { ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} } If there are n members in a set S i.e. cardinality of set |S| = n, then there are 2n subsets possible.Hence the power set would contain 2n elements. Or we can say that the cardinality of the power set is |P| is 2n. READ MORE...

Proper Subset

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 is represented as below A ⊂ B ( A is a proper subset of A )B ⊃ A ( B is a proper superset of A ) Examples ⇒ { x2 | x ∈ N } ⊂ N ( not all natural numbers are squares ){ 1, 2, 3 } ⊂ { 1, 2, 3, 4 }{ 1, 2, 3, 3 } ⊂ { 1, 2, 3, 4 } READ MORE...

Subset

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 is contained in B. B is called the superset of A. In the set theory, this relationship is depicted as below A ⊆ B ( A is a subset of B) B ⊇ A ( B is a superset of A ) ⇒ ∅ (empty set) is the subset of every set ⇒ A set S is a subset of itself. Examples ⇒ { 1 } ⊆ { 1, 2, 3 } ∅ ⊆ { 1, 2, 3 } { 1, 2, 3 } ⊆ { 1, 2, 3 } { x2 | x ∈ N […] READ MORE...

Equivalent Sets

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 also an element of A. If elements are repetitive in one set, then it is not required for it to repeat in the other set for the two sets to be equivalent. Examples ⇒ { 1, 2, 3 } ≡ { 1, 3, 2} { 1, 2, 3 } ≡ { 1, 3, 2, 2, 1, 2, 3, 3 } { 1, 2, 3 } ≢ { 1, 3, 2, 2, 1, 2, 3, 3, 4 } Since 4 is not in first set READ MORE...

Equal Sets

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 element appears n times in one set, then it must also appear n times in the other set. Mathematically, two sets A and B are equal if For each a ∈ A, there exists an element b ∈ B. n(A) = n(B) i.e. cardinality of A is equal to cardinality of B. Examples ⇒ { 1, 2, 3, 4 } = { 1, 3, 4, 2 } { 1, 1, 2, 2, 2, 4, 5 } = { 1, 4, 1, 2, 5, 2, 2 } { 1 ,2 ,3 ,4 } ≠ { […] READ MORE...

Finite Set

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 finite set S, n(S) is a finite number. ⇒ The standard mathematical sets like N, Z, R, etc. are all infinite. READ MORE...