Question

Given the sets A = {1, 2, 3}, B = {3, 4} C = {4, 5, 6} then A∪(B∩C) is

• A. {3}
• B. {1, 2, 3, 4}
• C. {1, 2, 4, 5}
• D. {1, 2, 3, 4, 5, 6}

Answer 1

The correct option is B {1, 2, 3, 4}

$B\cap C=\{3,4\}\cap \{4,5,6\}$
$\therefore B\cap C=\left\{4\right\}$
$A\cup (B\cap C)=\{1,2,3,4\}\cup \left\{4\right\}$
$\therefore A\cup (B\cap C)=\{1,2,3,4\}$

So, option b is correct.