Worksheet on Cardinal Number of a Set

Practice the set of questions given in the worksheet on cardinal number of a set. The question are based on finding the cardinal number of a set.


1. Write the cardinal number of each of the following sets:

(i) A = {0, 1, 2, 4}

(ii) B = {-3, -1, 1, 3, 5, 7}

(iii) C = { }

(iv) D = {3, 2, 2, 1, 3, 1, 2}

(v) E = {Natural numbers between 15 and 20}

(vi) F = {whole numbers from 8 to 14}

2. Given:             A = {Natural numbers less than 10}

                           B = {Letters of the word ‘PUPPET’}

                           C = {Squares of first four whole numbers}

                           D = {Odd numbers divisible by 2}

Find:

(i) n(A)

(ii) n(B)

(iii) n(C)

(iv) n(D)

(v) A ∪ B and n(A ∪ B)

(vi) A ∩ C and n(A ∩ C)

(vii) n(B ∪ D)

(viii) n(C ∩ D)

(ix) n(B ∪ C)

(x) n(A ∪ D)


3. Given: M = Set of letters in the word ‘ALLAHABAD’ and N = Empty set.

Find:

(i) n(M)

(ii) n(N)

(iii) n(M ∪ N)

(iv) n(M ∩ N)

(v) Is n(M) = n(M ∩ N)?

(vi) Is n(N) = n(M ∪ N)?

(vii) Is n(M) = n(M ∪ N)?


4. If A = {4, 8, 12, 16, 20}, B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} and C = {a, b, c, d, e}.

State, true or false:

(i) n(A) = n(C)

(ii) n(A) = n(B)

(iii) n(B) - n(C) = n(A)

(iv) n(B) =  2 ∙ n(C)


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


Answers:


1. (i) 4

(ii) 6

(iii) 0

(iv) 3

(v) 4

(vi) 7


2. (i) 9

(ii) 4

(iii) 4

(iv) 0

(v) {1, 2, 3, 4, 5, 6, 7, 8, 9, p, u, e, t}; 13

(vi) {1, 4, 9}; 3

(vii) 4

(viii) 0

(ix) 8

(x) 9


3. (i) 5

(ii) 0

(iii) 5

(iv) 0

(v) No, n(M) ≠ n(M ∩ N)

(vi) No, n(N) ≠  n(M ∪ N)

(vii) Yes, n(M) = n(M ∪ N)


4. (i) True

(ii) False

(iii) True

(iv) True

Sets and Venn-diagrams Worksheets

Worksheet on Set

Worksheet on Elements Form a Set

Worksheet to Find the Elements of Sets

Worksheet on Properties of a Set

Worksheet on Sets in Roster Form

Worksheet on Sets in Set-builder Form

Worksheet on Finite and Infinite Sets

Worksheet on Equal Sets and Equivalent Sets

Worksheet on Empty Sets

Worksheet on Subsets

Worksheet on Union and Intersection of Sets

Worksheet on Disjoint Sets and Overlapping Sets

Worksheet on Difference of Two Sets

Worksheet on Operation on Sets

Worksheet on Cardinal Number of a Set

Worksheet on Venn Diagrams



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