Table of Contents
What is the Cartesian product of a set with the empty set?
The Cartesian Product is the multiplication between two sets A and B, which produces ordered pairs. The Cartesian Product of any set with the empty set will always be empty because the empty set contains no elements.
Is a null set an infinite set?
Under this definition, because ∅ has no proper subsets, it cannot be infinite; hence it is finite.
What is the Cartesian product of a set with itself?
If X=Y, we can denote the Cartesian product of X with itself as X×X=X2. For examples, since we can represent both the x-axis and the y-axis as the set of real numbers R, we can write the xy-plane as R×R=R2.
What is the Cartesian product of a 12 and B AB?
Therefore, AxB ≠ BxA. If A = B then AxB is called the Cartesian Square of Set A and is represented as A2.
What is a finite and infinite set?
Finite sets are sets that have a fixed number of elements, are countable, and can be written in roster form. An infinite set is a set that is not finite, infinite sets may or may not be countable. This is the basic difference between finite sets and infinite sets.
What is null set example?
Any Set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ. Examples: Let A = {x : 9 < x < 10, x is a natural number} will be a null set because there is NO natural number between numbers 9 and 10.
What is meant by Cartesian product?
Definition of Cartesian product : a set that is constructed from two given sets and comprises all pairs of elements such that the first element of the pair is from the first set and the second is from the second set.
What is a subset of the Cartesian product?
Definition:A subset of the Cartesian product A x B is called a relation from the set A to the set B.
What is an example of a null set?
Examples: Let A = {x : 9 < x < 10, x is a natural number } will be a null set because there is NO natural number between numbers 9 and 10. Therefore, A = {} or φ
Is an empty set a finite number of elements?
An empty set is a set which has no element in it and can be represented as { } and shows that it has no element. As the finite set has a countable number of elements and the empty set has zero elements so, it is a definite number of elements.
What is the difference between finite and infinite sets?
Finite and Infinite Sets. Any set which is empty or contains a definite and countable number of elements is called a finite set. Sets defined otherwise, for uncountable or indefinite numbers of elements are referred to as infinite sets. Examples: