Question

If
A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

$$\begin{array}{cc}ColumnA& ColumnB\\ 1.A\cup B& a.\{3,4,6,7\}\\ 2.A\cap B& b.\varnothing \\ 3.(B\cap C)\cup D& c.\{3,4\}\\ 4.B\cup C\cup D& d.\{3,4,5,6,7,8,9,10\}\\ 5.(A\cap B)\cap (B\cup C)& e.\{1,2,3,4,5,6,7\}\\ & f.\{6,7,8,9,10\}\\ & g.\{7\}\end{array}$$

• A. 1 - e, 2 - c, 3 - f, 4 -d, 5-c
• B. 1 - e, 2 - c, 3 - f, 4 -d, 5-a
• C. 1 - b, 2 - a, 3 - c, 4 -e, 5-f
• D. 1 - b, 2 - a, 3 - c, 4 -e, 5-c

Answer 1

The correct option is A

1 - e, 2 - c, 3 - f, 4 -d, 5-c

A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

1. A ∪ B = {1, 2, 3, 4, 5, 6, 7}

2. A ∩ B = {3, 4}

3. B ∩ C = {6, 7}

(B ∩ C) ∪ D
= {6, 7} ∪ {7, 8, 9, 10}
= {6, 7, 8, 9, 10}

4. B ∪ C ∪ D = (B ∪ C) ∪ D

B ∪ C = {3, 4, 5, 6, 7, 8, 9}
(B ∪ C) ∪ D
= {3, 4, 5, 6, 7, 8, 9}∪{7, 8, 9,10}
= {3, 4, 5, 6, 7, 8, 9, 10}

5. (A ∩ B) ∩ (B ∪ C)
= {3, 4} ∩ {3, 4, 5, 6, 7, 8, 9}
= {3, 4}