NIMCET 2014 — Mathematics PYQ

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Question

NIMCET 2014 — Mathematics PYQ

NIMCET | Mathematics | 2014

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

Choose the correct answer:

Explanation

Concept:

$A \cup B$ means set of all the values in the set $A$ and $B$ .
$A \cap B$ is the set of common elements of $A$ and $B$ .

Calculation:

Given sets:

$A = \{(x, y) | y = 1/x, 0 \neq x \in R\}$ and $B = \{(x, y) | y = -x \in R\}$

For any value of $x \in R$ and $x \neq 0$ :

In set $A$ , the element will be $(x, 1/x)$ .
In set $B$ , the element will be $(x, -x)$ .

For $A \cap B$ :

\frac{1}{x} = -x

\Rightarrow x^{2} = -1

Which is not possible for any $x \in R$ .

\therefore A \cap B = \phi