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

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