JUPITER SCIENCE

A cartesian product between two sets is defined as the set consisting of all possible ordered pairs that can be formed by taking one element from each of the sets at a given time. If A and B are two sets such that a ∈ A and b ∈ B, then the cartesian product between A...

An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words, or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is...

The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B....

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 called a universal set. It provides a base set from which all of the sets of interest can be...

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 in only one of these subsets. ⇒ ∅ ( Empty Set ) cannot be the partition of any set. Examples ⇒ The set { 1, 2, 3 } can be...

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

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 ⇒ {...

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...

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...

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 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...

A set that has exactly one member is called a singleton set. { 1 } , { ‘a’ } , { x3 | x ∈ N , 2 < x < 3 } are all singleton sets.

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 designate an empty set. ⇒ Sometimes { ∅ } is also...

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 A.  Examples: The cardinality of the set { 1, 45, 2, 34 } is 4. The cardinality of...

The position of elements in a set does not change the value or the meaning of the set. The above statement signifies that { 1, 2, 3 } and { 1, 3, 2 } and { 2, 3, 1 } are all the same set. A set is primarily a collection and not a sequential representation of elements....

As defined earlier, a set is a collection or group of objects. These objects are called members of the Set. This relationship is represented by using the symbol ∈. The symbol ‘∈’ means “is a member of ” or “belongs to” or “is an element of”. The...

In mathematical terms, the members of sets are called elements. A set is represented by enlisting its member elements within curly brackets. There are three general conventions adopted for set representation – Roster, Ellipsis & Set-Builder form. Roster form...

What is a set? A Set is a collection of items. The collection can be either real-world objects or imaginary or theoretical entities. It can be a collection of numbers, alphabets, colors, countries’ names, etc.