Question

which of the following set has the cardinality equals to 5?
a. set A is the set of counting numbers less than 5
b. set B is the set of letters in the owrd "RACER".
c. set C is the set of positive ,ultiple of 5.
d. set D is the set of names of the fingers.

Answer 1

The set D of names of the fingers has the cardinality equals to 5

Given :

Four sets A , B , C , D

To find :

Which of the following set has the cardinality equals to 5

a. set A is the set of counting numbers less than 5

b. set B is the set of letters in the owrd "RACER".

c. set C is the set of positive multiple of 5.

d. set D is the set of names of the fingers.

Concept :

Cardinality of a set :

The cardinality of a set is defined as the total number of elements in the set.

Solution :

Step 1 of 3 :

Write down the given sets

Here the given four sets are A , B , C , D

A is the set of counting numbers less than 5

B is the set of letters in the owrd "RACER".

C is the set of positive multiple of 5.

D is the set of names of the fingers.

Step 2 of 3 :

Express the sets in roster form

We know that in roster form the elements are enclosed in curly brackets after separating them by commas

A is the set of counting numbers less than 5

∴ A = { 1 , 2 , 3 , 4 }

B is the set of letters in the owrd "RACER".

∴ B = { R , A , C , E }

C is the set of positive multiple of 5.

∴ C = { 5 , 10 , 15 , 20 , . . . . . }

D is the set of names of the fingers.

∴ D = { Thumb finger , Index finger , Middle finger , Ring finger , Little finger }

Step 3 of 3 :

Choose the correct option

We know that cardinality of a set is defined as the total number of elements in the set.

A = { 1 , 2 , 3 , 4 }

∴ Cardinality of A = 4

So option a is not correct

B = { R , A , C , E }

∴ Cardinality of B = 4

So option b is not correct

C = { 5 , 10 , 15 , 20 , . . . . . }

C is an infinite set

∴ Cardinality of C is ∞

So option c is not correct

D = { Thumb finger , Index finger , Middle finger , Ring finger , Little finger }

∴ Cardinality of D = 5

So option d is correct

Hence the correct option is d. set D is the set of names of the fingers.

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