In practice test on operations on sets we will solve 8 different types
of questions on more about sets. The questions will be mainly related to
**union of sets**, **intersection of sets** and **difference of sets**.

Practice Test on Operations on Sets

**1. If A = {2, 3, 4, 5} B = {4, 5, 6, 7} C = {6, 7, 8, 9} D = {8, 9, 10, 11}, find **

(a) A ∪ B

(b) A ∪ C

(c) B ∪ C

(d) B ∪ D

(e) (A ∪ B) ∪ C

(f) A ∪ (B ∪ C)

(g) B ∪ (C ∪ D) **2. If A = {4, 6, 8, 10, 12} B = {8, 10, 12, 14} C = {12, 14, 16} D = {16, 18}, find **

(a) A ∩ B

(b) B ∩ C

(c) A ∩ (C ∩ D)

(d) A ∩ C

(e) B ∩ D

(f)(A ∩ B) ∪ C

(g) A ∩ (B ∪ D)

(h) (A ∩ B) ∪ (B ∩ C)

(i) (A ∪ D) ∩ (B ∪ C) **3. If A = {4, 7, 10, 13, 16, 19, 22} B = {5, 9, 13, 17, 20} C = {3, 5, 7, 9, 11, 13, 15, 17} D = {6, 11, 16, 21} then find **

(a) A - C

(b) D - A

(c) D - B

(d) A - D

(e) B - C

(f) C - D

(g) B - A

(h) B - D

(i) D - C

(j) A - B

(k) C - B

(l) C - A

More Practice Test on Operations on Sets

(a) A = The set of all letters of the word FEAST

B = The set of all letters of the word TASTE

(b) A = {x : x ∈ W, 0 < x ≤ 7}

B = {x : x ∈ W, 4 < x < 9}

(c) A = {x | x ∈ N, x is a factor of 12}

B = {x | x ∈ N, x is a multiple of 2, x < 12}

(d) A = The set of all even numbers less than 12

B = The set of all odd numbers less than 11

(e) A = {x : x ∈ I, -2 < x < 2}

B = {x : x ∈ I, -1 < x < 4}

(f) A = {a, l, m, n, p}

B = {q, r, l, a, s, n}

(a) (X - Y) ∪ (Y - X)

(b) (X - Y) ∩ (Y - X)

(c) (Y - Z) ∪ (Z - Y)

(d) (Y - Z) ∩ (Z - Y)

Practice Test on Operations on Sets

**7. Let ξ = {1, 2, 3, 4, 5, 6, 7} and A = {1, 2, 3, 4, 5} B = {2, 5, 7} show that **

(a) (A ∪ B)' = A' ∩ B'

(b) (A ∩ B)' = A' ∪ B'

(c) (A ∩ B) = B ∩ A

(d) (A ∪ B) = B ∪ A

**8. Let P = {a, b, c, d} Q = {b, d, f} R = {a, c, e} verify that**

(a) (P ∪ Q) ∪ R = P ∪ (Q ∪ R)

(b) (P ∩ Q) ∩ R = P ∩ (Q ∩ R)

Answers for practice test on operations on sets are given below to check the correct answers.

**Answers: **

**1.** (a) {2, 3, 4, 5, 6, 7}

(b) {2, 3, 4, 5, 6, 7, 8, 9}

(c) {4, 5, 6, 7, 8, 9}

(d) {4, 5, 6, 7, 8, 9, 10, 11}

(e) {2, 3, 4, 5, 6, 7, 8, 9}

(f) {2, 3, 4, 5, 6, 7, 8, 9}

(g) {4, 5, 6, 7, 8, 9, 10, 11}

**2. **(a) {8, 10, 12}

(b) {12, 14}

(c) ∅

(d) {12}

(e) d

(f) {8, 10, 12, 14, 16}

(g) {8}

(h) {8, 10, 12, 14}

(i) {8, 10, 12, 16} **3.** (a) {4, 10, 16, 19, 22}

(b) {6, 11, 21}

(c) {6, 11, 16, 21}

(d) {4, 7, 10, 13, 19, 22}

(e) {20}

(f) {3, 5, 7, 9, 13, 15, 17}

(g) {5, 19, 17, 20}

(h) {5, 9, 13, 17, 20}

(i) {6, 16, 21}

(j) {4, 7, 10, 16, 19, 22}

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

(l) {3, 5, 9 11, 15, 17}

**4. **B **5.** (a) {F, E, A, S, T}, {E, A, S, T}, {F}

(b) {1, 2, 3, 4, 5, 6, 7, 8}, {5, 6, 7}, {1, 2, 3, 4}

(c) {1, 2, 3, 4, 6, 8, 10, 12}, {2, 4, 6}, {1, 3, 12}

(d) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, d, {2, 4, 6, 8, 10}

(e) {-1, 0, 1, 2, 3}, {0, 1}, {-1}

(f) {a, 1, m, n, p, q, r, s}, {a, l, n}, {m, p} **6.** (a) {2, 3, 5, 6, 7, 8}

(b) d

(c) d {3, 4, 5, 6}

(d) d**7.** (a) L.H.S. = R. H. S = {6}

(b) L.H.S. = R. H. S = {1, 3, 4, 6, 7}

(c) {2, 5}

(d) {1, 2, 3, 4, 5, 7}**8. **(a) {a, b, c, d, e, f}

(b) d

● **Set Theory**

● **Sets**

● **Subset**

● **Practice Test on Sets and Subsets**

● **Problems on Operation on Sets**

● **Practice Test on Operations on Sets**

● **Venn Diagrams in Different Situations**

● **Relationship in Sets using Venn Diagram**

● **Practice Test on Venn Diagrams**

**8th Grade Math Practice**

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