First slide

Operations on Sets

Question

Let X and Y be two sets.
Statement 1: $X \cap (Y \cup X)^{'} = ϕ$
Statement 2: If $X \cup Y$ has m elements and $X \cap Y$ has n elements then symmetric difference $X ∆ Y$ has $m - n$ elements.

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

$X \cap (Y \cup X)^{'} = X \cap (Y^{'} \cap X^{'}) = X \cap X^{'} \cap Y^{'} = ϕ$
Statement-1 is True.
$X Δ Y = (X ~ Y) \cup (Y ~ X) = (X \cup Y) ~ (X \cap Y)$
$\Rightarrow$ number of elements in $X ∆ Y = m - n .$
$\Rightarrow$ Statement-2 is True but does explain statement-1.

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