First slide

Introduction to Relations (XI) on Sets

Question

Let A = {1, 2, 3} and B = {3, 8}
Statement-1: $(A \cup B) \times (A \cap B) = {(1, 3), (2, 3), (3, 3) (8, 3)}$
Statement-2: $(A \times B) \cap (B \times A) = {(3, 3)}$

Moderate

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C

STATEMENT-1 is True, STATEMENT-2 is False
D

STATEMENT-1 is False, STATEMENT-2 is True

Solution

$A \cup B = {1, 2, 3, 8}, A \cap B = {3}$
$\Rightarrow (A \cup B) \times (A \cap B) = {(1, 3), (2, 3), (3, 3), (8, 3)}$
$\Rightarrow$ Statement-1 is True .
$\begin{array}{l} (x, y) \in (A \times B) \cap (B \times A) \\ \Rightarrow (x, y) \in A \times B and (x, y) \in B \times A \\ \Rightarrow x \in A \cap B, y \in A \cap B \end{array}$
$\Rightarrow {(3, 3)} = (A \times B) \cap (B \times A) \Rightarrow$ Statement-2 is also true but is not a correct explanation for statement-1.

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