Choose the correct answers from the given four option: If sets A and B are defined as…

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

  1. \(\text{A}\cap\text{B}=\text{A}\)

  2. \(\text{A}\cap\text{B}=\phi\)

  3. \(\text{A}\cap\text{B}=\text{B}\)

  4. \(\text{A}\cup\text{B}=\text{A}\)

Solution

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

Asked in: NCERTEXAMPLER

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