First slide

Operations on Sets

Question

If the sets A and B are defined as
$A = {(x, y) ∣ y = 1 / x, x \neq 0, x \in R}$
$B = {(x, y) ∣ y = - x, x \in R,}$ Then

Moderate

A

$A \cap B = A$
B

$A \cap B = B$
C

$A \cap B = ϕ$
D

$A \cup B = A$

Solution

For, $A \cap B$ we have
$- x = \frac{1}{x}$
$\Rightarrow - x^{2} = 1$
$\Rightarrow x^{2} = - 1$ , which is not possible
$∴ A \cap B = ϕ$

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