Question

Let A = set of natural numbers less than 8, B = {even natural numbers less than 12} C = {Multiples of 3 between 5 and 15},and D = {Multiples of 4 greater than 6 and less than 20}; Find: 1. (B ∩ D) B ∪ C 2. A ∪ D 3. C ∪ D 4. A ∩ C 5. (B ∩ C) ∪ A 6. (D ∪ A) ∩ B 7. (A ∩ C) ∪ 8. (B ∪ D) ∩ (C ∪ A)​

Answer 1

Step-by-step explanation:

Write down the union and intersection of the following pairs of sets:

(i) A = {1, 2, 3, 4, 5, 6}

B = {1, 3, 5, 7, 9}

(ii) X = {a, b, c, d, e}

Y = {c, e, f, g}

(iii) P = {x : x is a multiple of 2 between 9 and 21}

Q = {x : x is a multiple of 3 between 10 and 20}

(iv) M = {letters in the word ‘COMPUTER’}

N = {letters in the word ‘CALCULATOR’}

2. Let A = set of natural numbers less than 8,

B = {even natural numbers less than 12}

C = {Multiples of 3 between 5 and 15}

and D = {Multiples of 4 greater than 6 and less than 20};

Find:

(i) B ∪ C

(ii) A ∪ D

(iii) C ∪ D

(iv) A ∩ C

(v) (B ∩ C) ∪ A

(v) (D ∪ A) ∩ B

(vii) (A ∩ C) ∪ (B ∩ D)

(viii) (B ∪ D) ∩ (C ∪ A)

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

Answers:

1. (i) A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9};

A ∩ B = {1, 3, 5}

(ii) X ∪ Y = {a, b, c, d, e, f, g}

X ∩ Y = {c, e}

(iii) P ∪ Q = {10, 12, 14, 15, 16, 18, 20}

P ∩ Q = {12, 18}

(iv) M ∪ N = {c, o, m, p, u, t, e, r, a, l}

M ∩ N = {c, u, t, o, r}

2. (i) {2,4, 6, 8, 9, 10, 12}

(ii) {1, 2, 3, 4, 5, 6, 7, 8, 12, 16}

(iii) {6, 8, 9, 12, 16}

(iv) {6}

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

(vi) {2, 4, 6, 8}

(vii) {6, 8}

(viii) {2, 4, 6, 12}