Worksheet on Operation on Sets

Worksheet on operation on sets we will solve 10 different types questions on math sets.

1. Find the union of each of the following pairs of sets.

(a) A = {2, 4, 6}

     B = {1, 2, 3}

(b) P = {a, e, i, o, u}

    Q = {a, b, c, d}

(c) X = {x : n ∈ N, x = 2n, n < 4}

     Y = {x : x is an even number less than 10}

(d) M = {x : x is natural number and multiple of 3}

     N = {x : x is a prime number less than 19}

(e) D = {x : x is an integer -3 < x < 3}

     E = {x : x is a factor of 8}

(f) G = {x : x ∈ N, x < 7}

     H = {x : x ∈ Z, -2 ≤ x ≤ 3}


2. Find the intersection of each of the following pairs of sets.

(a) A = {1, 4, 9, 16}

     B = {3, 6, 9, 12}

(b) C = {p, q, r, s}

     D = {a, b}

(c) P = {x : n ∈ N, x = 3n   n< 3}

    Q = {x : x ∈ N   x < 7}

(d) X = {x : x is a letter of the word ‘LOYAL’}

     Y = {x : x is a letter in the word ‘FLOW’}

(e) G = {x : x = n2, when n ∈ N}

     H = {x : x = 4n, when n ∈ W   n < 5}

3. If P = {1, 2, 3}   Q = {2, 3, 4}   R = {3, 4, 5}   S = {4, 5, 6}, find

(a) P ∪ Q

(b) P ∪ R

(c) Q ∪ R

(d) Q ∪ S

(e) P ∪ Q ∪ R

(f) P ∪ Q ∪ S

(g) Q ∪ R ∪ S

(h) P ∩ Q

(i) P ∩ R

(j) Q ∩ R

(k) Q ∩ S

(l) P ∩ Q ∩ R

(m) P ∩ Q ∩ S

(n) Q ∩ R ∩ S


4. If A = {a, b, c, d}   B = {b, c, d, e}   C = {c, d, e, f}   D = {d, e, f, g}, find

(a) A - B

(b) B - C

(c) C - D

(d) D - A

(e) B - A

(f) C - B

(g) D - C

(h) A - D


5. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6, 8, 10}
B = {1, 3, 5, 7, 8, 9}

Find:

(a) A'

(b) B'

(c) A' ∪ B'

(d) A' ∩ B'

(e) (A ∪ B)'

Also show (A ∪ B)' = A' ∩ B'.


6. Find the complement of the following sets if universal set is the set of natural numbers.

(a) {x : x is a prime number}

(b) {x : x is a multiple of 2}

(c) {x : x is a perfect cube}

(d) {x : x ≥ 10}

(e) {x : x Є N, 5x + 1 > 20}

(f) {x : x is an odd natural number}

Worksheet on Operation on Sets
7. If U = {a, b, c, d, e, f} find the complement of the following.

(a) A = { }

(b) B = {c, d, f}

(c) D = {a, b, c, d, e, f}

(d) C = {a, b, d}

(e) E = {b, c}

(f) F = {a, c, f}


8. If U = {1, 2, 3, 4, 5, 6} and A = {2, 3, 6}, find

(a) A ∪ A'

(b) ∅ ∩ A

(c) A ∩ A'

(d) U' ∩ A


9. Let P = {1, 3, 5, 7}   Q = {3, 7, 9, 11}   R = {1, 5, 8, 11}, then verify the following.

(a) P ∪ Q = Q ∪ P

(b) (P ∪ Q) ∪ R = P ∪ (Q ∪ R)

(c) P ∩ Q = Q ∩ P

(d) (P ∩ Q) ∩ R = P ∩ (Q ∩ R)

(e) P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R)

(f) P ∩ (Q ∪ R) = (P ∩ Q) ∪ (P ∩ R)

Worksheet on Operation on Sets
10. Let U = {a, b, c, d, e, f, g},   A = {a, c ,f , g},   B = {f, g, b, d}

Verify:

(a) (A ∪ B)' = (A' ∩ B')

(b) (A ∩ B)' = (A' ∪ B')


Answers for worksheet on operation on sets are given below so that students can check the answers.

Worksheet on Operation on Sets Answers:


1. (a) {1, 2, 3, 4, 6}
(b) {a, b, c, d, e, i, o, u}
(c) {2, 4, 6, 8}
(d) {2, 3, 5, 7, 9, 11, 13, 17, 6, 9, 12, 15, ….}
(e) {-2, -1, 0, 1, 2, 4, 8}
(f) {-2, -1, 0, 1, 2, 3, 4, 5, 6}


2. (a) {9}
(b) d
(c) {3, 6}
(d) {L, O}(e) {4, 16}


3. (a) {1, 2, 3, 4}
(b) {1, 2, 3, 4, 5}
(c) {2, 3, 4, 5}
(d) {2, 3, 4, 5, 6}
(e) {1, 2, 3, 4, 5}
(1) {1, 2, 3, 4, 5, 6}
(g) {2, 3, 4, 5, 6}
(h) {2, 3}
(i) {3}
(j) {3, 4}
(k) {4}
(l) {3}
(m) ∅
(n) {4}


4. (a) {a}
(b) {b}
(c) {c}
(d) {e, f, g}
(e) {e}
(f) {f }
(g) {g}
(h) {a, b, c}


5. {3, 5, 7, 9}
(b) {2, 4, 6, 10}
(c) {2, 3, 4, 5, 6, 7, 9, 10}
(d) {∅}


6. (a) {x : x is composite number and 1}
(b) {x : x is odd}
(c) {x : x is not a perfect cube}
(d) {x : x < 10, x ∈ N}
(e) {x : x ∈ N and x < 4}
(f) {x : x is even}


7. (a) U
(b) {a, b, e}
(c) ∅
(d) {c, e, f}
(e) {a, d, e, f}
(f) {b, d, e}


8. (a) U
(b) A
(c) ∅
(d) ∅

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