Worksheet to Find the Cardinal Number of the Sets

Worksheet to find the cardinal number of the sets will help us to practice different types of questions on finding the cardinal number of the given set.

We know, the number of distinct elements in a finite set is called its cardinal number.

1. If A {5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10};

Find:

(i) n(A) + n(B)

(ii) n(A ∪ B)

(iii) n(A ∩ B)

(iv) n(A ∪ B) + n(A ∩ B)

(v) n(B ∪ C)

(vi) n(B) + n(C) – n(B ∩ C)

(vii) Is n(A) + n(B) = n(A ∪ B) + n(A ∩ B)?

(viii) Is n(B ∪ C) = n(B) + n(C) - n(B ∩ C)?

2. State, whether each of the following is true or false. In case, it is false, write the correct answer.

(i) If A = {0}, then n(A) = 0.

(ii) n(∅) = 1.

(iii) If T = {a, l, a, h, b, d, h}; then n(T) = 5

(iv) If B = {1, 5, 51, 15, 5, 1}; then n(B) = 6

3. Find the cardinal number of the following sets:

(i) {  }

(ii) {0}

(iii) {3, 7, 11, 15}

(iv) {3, 3, 3, 4, 4, 5}

(v) {x : x is a letter in the word ‘STATISTICS’}

(vi) {x : x is an odd whole number less than 12}

(vii) {x : x ∈ N and x$$^{2}$$ < 50}

(viii) {x : x is a factor of 12}

4. If O = {odd numbers less than 12} and E = {even numbers between 7 and 17}, show that:

n(O) – n(E)  = 1.

Answers for the worksheet to find the cardinal number of the sets are given below to check the exact answers of the above set of questions.

1. (i) 8

(ii) 7

(iii) 1

(iv) 8

(v) 7

(vi) 7

(vii) Yes, n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

(viii) Yes, n(B ∪ C) = n(B) + n(C) - n(B ∩ C)

2. (i) False; n(A) = 1

(ii) False; n(∅) = 0.

(iii) True

(iv) False; n(B) = 4.

3. (i) 0

(ii) 1

(iii) 4

(iv) 3

(v) 5

(vi) 6

(vii) 7

(viii) 6

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