# cardinality dealing with equal or equivalent sets?

#### Gertie

##### New member
I have a specific problem that I cannot figure out.
Question: A=is a set of residents age 61 or older living in the U.S.
B=is a set of residents age 61 or older registered to vote in the U.S.
Are these sets equal, equivalent, or both?

Gertie

#### Subhotosh Khan

##### Super Moderator
Staff member
Gertie said:
I have a specific problem that I cannot figure out.
Question: A=is a set of residents age 61 or older living in the U.S.
B=is a set of residents age 61 or older registered to vote in the U.S.
Are these sets equal, equivalent, or both?

Gertie
What are the conditions under which:

Two sets are equal

and

Two sets are equivalent

#### Gertie

##### New member
Cardinality deals with the number of elements in each set. If set A=4 humans and set B=4 animals then the sets are equivalent with 4 in each set, but they are not equal because they are not identical. another example would be A=(A,B,C) and set B=(A,B,C) they are equal and equivalent. Also, if an element is repeated in a set, then it is only counted once. example A=(A,B,B,C,C,C) this set still has only 3 elements because you only count (A,B,C) once. Thank you

#### Subhotosh Khan

##### Super Moderator
Staff member
Excellent!

Now tell me for the given problem:

Does A and B have same number of elements?