CARDINAL NUMBER OF A SET WORKSHEET

Here we are going to see some practice questions on cardinal number of a set.

Cardinal number of a set :

The number of elements in a set is called the cardinal number of the set.

The cardinal number of the set A is denoted by n(A).

Cardinal number of a set worksheet - Practice questions

(1)  Find the cardinal number of the following set 

A = { -1, 0, 1, 2, 3, 4, 5, 6}

(2)  Find the cardinal number of the following set 

A = {x : x is a prime factor of 12}

(3)  Find the cardinal number of the following set 

B = {x : x ∈ W, x ≤ 5}

(4)  Find the cardinal number of the following set 

C = {x : x = 5ⁿ, n ∈ N and n < 5}

(5)  Find the cardinal number of the following set 

D = {x : x is a consonants in English alphabets}

(6)  Find the cardinal number of the following set 

E = { x : x is even prime number }

(7)  Find the cardinal number of the following set 

E = { x : x < 0, x ∈ W }

(8)  Find the cardinal number of the following set 

Q = { x : - 3 ≤ x ≤ 5, x ∈ Z }

Cardinal number of a set worksheet - Solution

Question 1 :

Find the cardinal number of the following set 

A = { -1, 0, 1, 2, 3, 4, 5, 6}

Solution :

Number of elements in the given set is 7.

So, cardinal number of set A is 7.

That is n (A) = 7.

Question 2 :

Find the cardinal number of the following set 

A = {x : x is a prime factor of 12}

Solution :

To find the cardinal number of the given set, we have to count the number of elements of the set.

So, first we have to list out the elements of the set.

Factor of 12 is 1, 2, 3, 4, 6 and 12.

But prime factor of 12 are 2 and 3.

A = {2, 3}

The given set has 2 elements. Hence n(A) = 2.

Question 3 :

Find the cardinal number of the following set 

B = {x : x ∈ W, x ≤ 5}

Solution :

Here "W" stands for whole numbers.

The set contains whole numbers those are equal to 5 or less than 5.

B = {0, 1, ,2, 3, 4, 5}

Set B has 6 elements. Hence n(B) = 6.

Question 4 :

Find the cardinal number of the following set 

C = {x : x = 5ⁿ, n ∈ N and n < 5}

Solution :

We may find the elements of the above set using the pattern x = 5ⁿ 

Question 5 :

Find the cardinal number of the following set 

D = {x : x is a consonants in English alphabets}

Solution :

In English alphabets other than vowels is known as consonants.

D = { b, c, d, f, g, h, j, k , l, m, n, p, q, r, s, t, v, w, x, y, z}  

Total number of elements in set D is 21.

Hence, n (D) = 21

Question 6 :

Find the cardinal number of the following set 

E = { x : x is even prime number }

Solution :

A number which is divisible by 1 and itself is known as prime number. Among prime numbers there is only one even prime number

That is,

E = { 2 }

Total number of elements in set E is 1.

Hence, n (E) = 1

Question 7 :

Find the cardinal number of the following set 

E = { x : x < 0, x ∈ W }

Solution :

A number which is less than zero is negative number and it will not be a whole number.

So, the above set will not contain any elements.

Hence n (E) = 0.

Question 8 :

Find the cardinal number of the following set 

Q = { x : - 3 ≤ x ≤ 5, x ∈ Z }

Solution :

The elements of the set Q lies between -3 and 5.We may take -3 and 5 also. 

Q =  { -3, -2, -1, 0, 1, 2, 3 } 

Number of elements in the above set is 7.

Hence n (Q) = 7.

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