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) ∅

Worksheet on Operation on Sets

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**● **Worksheet on
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**● **Worksheet on
Union and Intersection of Sets

**● **Worksheet on
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**● **Worksheet on Difference of Two Sets

**● **Worksheet on Operation on Sets

**● **Worksheet on Cardinal Number of a Set

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