First slide

Operations on Sets

Question

If $A = \{(x, y) : y = \frac{4}{x}, 0 \neq x \in R\}$ and $B = {(x, y) : y = x, x > 0, x \in R}$

Moderate

A

$A \cap B = ϕ$
B

$A \cap B is singleton set$
C

$A \cap B has infinite elements$
D

$A \cap B has two elements$

Solution

Given, $A = \{(x, y) : y = \frac{4}{x}, 0 \neq x \in R\} \Rightarrow A$ is the set of all points on the graph of xy = 4
and $B = {(x, y) : y = x, x > 0, x \in R}$
$\Rightarrow$ B is the set of all points on the Graph of y = x, x>0
Now, we plot the graph of given sets.
Since' the graph of xy = 4 and y = x, x> 0 intersect at one point.
$∴ A \cap B \neq ϕ and A \cap B$ is a singleton set.

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