Question

Types of sets
Write their names ​

Answer 1

Answer:

there are Five types of sets

1. singleton sets

2. empty sets or null set

3.finite set

4.infinite set.

5.equal set

Answer 2

Answer:

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1. Singleton set  

If a set contains only one element it is called to be a singleton set.

Hence the set given by {1}, {0}, {a} are all consisting of only one element and therefore are singleton sets.

2. Finite Set

A set consisting of a natural number of objects, i.e. in which number element is finite is said to be a finite set. Consider the sets

A = { 5, 7, 9, 11} and B = { 4 , 8 , 16, 32, 64, 128}

Obviously, A, B contain a finite number of elements, i.e. 4 objects in A and 6 in B. Thus they are finite sets.

3. Infinite set

If the number of elements in a set is finite, the set is said to be an infinite set.

Thus the set of all natural number is given by N = { 1, 2, 3, ...} is an infinite set. Similarly the set of all rational number between ) and 1 given by

A = {x:x E Q, 0 <x<1} is an infinite set.

4. Equal set

Two set A and B consisting of the same elements are said to be equal sets. In other words, if an element of the set A sets the set A and B are called equal i.e. A = B.

5. Null set/ empty set

A null set or an empty set is a valid set with no member.  

A = { } / phie cardinality of A is 0.

There is two popular representation either empty curly braces { } or a special symbol phie. This A is a set which has null set inside it.

6. Subset

A subset A is said to be subset of B if every elements which belongs to A also belongs to B.

   A = { 1, 2, 3}

   B = { 1, 2, 3, 4}

   A subset of B.

7. Proper set

A set is said to be a proper subset of B if A is a subset of B, A is not equal to B or A is a subset of B but B contains at least one element which does not belong to A.

8. Improper set

Set A is called an improper subset of B if and Only if A = B. Every set is an improper subset of itself.

9. Power set

Power set of a set is defined as a set of every possible subset. If the cardinality of A is n than Cardinality of power set is 2^n as every element has two options either to belong to a subset or not.

10. Universal set

Any set which is a superset of all the sets under consideration is said to be universal set and is either denoted by omega or S or U.

   Let  A = {1, 2, 3}

   C = { 0, 1} then we can take

   S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} as universal set.

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