Write are different types of sets? Explain them with examples.
Answers
Types Of Sets and Explanation Of Each:
Finite Set: In this type of set there is countable number of elements. We can count the number of elements in this set very easily.
For Example: C = {1, 2, 3, 4, 5}
Infinite Set: In this type of set the elements are uncountable. It may go up to infinity. There is a large number of elements in this set. T
For Example: The set of entire whole numbers, The set of entire natural numbers etc.
Empty Set: In this type of set there would be no elements it is called as void set or null set.
For Example: C = {}
Singleton Set: In this type of set there would be only one element. This is the reason why it is called as singleton set.
For Example: C = {1}
Equivalent Set: If two sets are equal to each other having the same number of elements then the set is said to be an equivalent set but the elements in this set can be different.
For Example: n(A) = n(B)
Equal Set: These set have exactly same element even though they maybe in different order still the elements in both these sets would be same.
For Example: A = {a, c, t} B = {c, a, t} C = {t, a, c} All three of these sets are equal sets.
Subset: In this type of set all elements are contained in another set. All elements of A are elements of B.
For Example: The parent set = {1, 2, 3, 4, 5} Then {1, 2, 3} is a subset and {3,4} is also a subset.
Superset: Superset is directly the opposite of subset in this type of set all the elements of B are the elements of A.
For Example: C = {1,3,5} then D = {1,3,4,5} is a proper superset of C.
Proper Subset: In this type of set A is a subset of B but A is not equal to B then A is a proper subset of B.
For Example: C={1,3,5} then B={1,5} is a proper subset of C.
Power Set: The set which is a subset of A is a power set of A
Universal Set: We consider a set that is the superset of all set under this consideration it is called as a universal set.
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