Choose the correct answers from the given four option: If sets A … - Vidyadip

MCQ

Choose the correct answers from the given four option: If sets A and B are defined as $\text{A}=\Big\{(\text{x},\text{y})|\text{y}=\frac{1}{\text{x}},0\neq\text{x}\in\text{R}\Big\}\ \text{B}=\{(\text{x},\text{y})|\text{y}=-\text{x},\text{x}\in\text{R}\},$ then

A
$\text{A}\cap\text{B}=\text{A}$
B
$\text{A}\cap\text{B}=\text{B}$
✓
$\text{A}\cap\text{B}=\phi$
D
$\text{A}\cup\text{B}=\text{A}$

✓

Answer

Correct option: C.

$\text{A}\cap\text{B}=\phi$

Given that: $\text{A}=\Big\{(\text{x},\text{y}|\text{y}=\frac{1}{\text{x}},0\neq\text{x}\in\text{R}\Big\},$
and $\text{B}=\big\{(\text{x},\text{y}|\text{y}=\text{x},\text{x}\in\text{R}\big\}$
It is very clear that $\text{y}=\frac{1}{\text{x}}$ and y = -x
$\because \frac{1}{\text{x}}\neq -\text{x}$
$\therefore \text{A}\cap\text{B}=\phi$
Hence, the correct option is (c).

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