terminologies of set

Terminologies of Set

1. Unit Set

2. Empty set or Null set

3. Finite set

4. Infinite set

5. Cardinal Number

6. Equal sets

7. Equivalent sets

8. Universal set

9. Joint Sets

10.Disjoint Sets

1.Unit Set

a set that contains only one element.

(illustration) unit set

A={ 1 }; B={ c }; C={ banana }

2.Empty set or Null set

is a set that has no element.

(illustration) empty or null set

A={ }

A set of seven yellow carabaos

3. Finite set

a set that the elements in a given set is countable.

4. infinite set

a set that elements in a given set has no end or not countable.

(illustration) infinite sets

A set of counting numbers

A={...-2,-1,0,1,2,3,4,...}

(illustration) finite set

A={ 1,2,3,4,5,6 }

B={ a,b,c,d }

5. Cardinal Number

are numbers that used to measure the number of elements in a given set. It is just similar in counting the total number of element in a set.

(illustration) Cardinal number

A={ 2,4,6,8 } n=4

B={ a,c,e } n=3

6. Equal sets

Two sets, say A and B, are said to be equal if and only if they have equal number of cardinality and the element/s are identical. There is a 1-1 correspondence.

(illustration) equal set

A={ 1,2,3,4,5 } B={ 3,5,2,4,1 }

7. Equivalent sets

Two sets, say A and B, are said to be equivalent if and only if they have the exact number of element. There is a 1- 1 correspondence.

(illustration) equivalent set

A={ 1,2,3,4,5 } B={ a,b,c,d,e }

8. Universal set

U is the set of all elements under discussion.

(illustration) universal set

A set of an English alphabet

U={ a,b,c, d,..., z }

9. Joint Sets

Two sets, say A and B, are said to be joint sets if and only if they have common element/s.

(illustration) joint set

A={ 1,2,3 } B={ 2,4,6 }

Here, sets A and B are joint set since they have common element such as 2.

10.Disjoint Sets

Two sets, say A and B, are said to be disjoint if and only if they are mutually exclusive or if they don't have common element/s.

(illustration) disjoint sets

A={ 1,2,3 } B={ 4,6,8 }

Subset of a Set

Set A is a subset of B, denoted by ⊆ , if and only if all elements of A are also elements of B.

number of subsets =

2n

(example) Subsets of A:

A={x,y,z}

{ },{ x },{ y },{ z },{ x,y },{ x,z },{ y. z },{ x,y, z }

Proper subset

A proper subset of a set A is a subset of A that is not equal to A. In othey words, if Bis a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

proper subset example

if A={1,3,5} then B={1,5} is a proper subset of A. The set C={1, 3, 5} is a subset of A, but it is not a proper subset of A since C= A. The set D={1, 4} is not even a subset of A, since 4 is not an element of A.