Question

If the sets $A$ and $B$ are defined as

$A=\left\{\right(x,y):y=\frac{1}{x},x\in R-\{0\left\}\right\}$

$B=\left\{\right(x,y):y=-x,x\in R\}$, then

• A. $A\cap B=A$
• B. $A\cap B=B$
• C. $A\cap B=\varnothing$
• D. None of these

Answer 1

The correct option is C

$A\cap B=\varnothing$

It is given that

$A=\left\{\right(x,y):y=\frac{1}{x},x\in R-\{0\left\}\right\}$

$B=\left\{\right(x,y):y=-x,x\in R\}$

As $A\cap B$ is set of ordered pairs of $(x,y)$ for which curves $y=\frac{1}{x}$ and $y=-x$ intersects each other.

For the points of intersection, we have $-x$ = $\frac{1}{x}$
⇒ $x^2=-1$,

which does not give any real value of $x$, so there is no point of intersection.

Hence, $A\cap B=\varnothing$.