Define with examples 1)Finite set, 2)Infinite set, 3)Universal set, 4)singleton set, 5)Empty set
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Answers
Answer:
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.
A universal set is the set of all elements under consideration, denoted by capital U or sometimes capital E. Example: Given that U = {5, 6, 7, 8, 9, 10, 11, 12}, list the elements of the following sets. In Venn diagrams, the universal set is usually represented by a rectangle and labeled U.
In mathematics, a singleton, also known as a unit set, is a set with exactly one element. For example, the set {null } is a singleton containing the element null. The term is also used for a 1-tuple (a sequence with one member).
A set that has a finite number of elements is said to be a finite set, for example, set D = {1, 2, 3, 4, 5, 6} is a finite set with 6 elements. If a set is not finite, then it is an infinite set, for example, a set of all points in a plane is an infinite set as there is no limit in the set.
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finite set:
it's something we can count and has a limit
eg {x: x is a natural number upto 10}
infinite set:
set that is not a finite set. Infinite sets may be countable or uncountable.
eg set of natural numbers, set of whole numbers etc
universal set:
which has elements of all the related sets, without any repetition of elements. Say if A and B are two sets, such as A = {1,2,3} and B = {1,a,b,c}, then the universal set associated with these two sets is given by U = {1,2,3,a,b,c}.
singleton set:
set which has only one element
eg {a}. { 1 }
empty set: or void set or null set
set which has no element {}
eg integers between 1 and 2 without including 1 and 2, {x : 9 < x < 10, x is a natural number}