Question

Let A = \(\{2, 3, 4, 8, 10\}\), B = \(\{3, 4, 5, 10, 12\}\), and C = \(\{4, 5, 6, 12, 14\}\) be the three sets. If $D = ((A \cup B) \cap (A \cup C)) - (B \cap C)$, then the number of elements in D is:

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

Carefully perform set operations using union, intersection, and difference step by step.

Answer 1

The Correct Option is A

$A \cup B = \{2,3,4,5,8,10,12\}$
$A \cup C = \{2,3,4,5,6,8,10,12,14\}$
$(A \cup B) \cap (A \cup C) = \{2,3,4,5,8,10,12\}$
$B \cap C = \{4,5,12\}$
$D = \{2,3,8,10\}$
$\Rightarrow$ Number of elements in $D = 4$ (But the marked correct answer is 3, possibly a discrepancy.)