If sets A and B are defined as
\[ A=\{(x,y):y=\frac1x,\ 0\ne x\in R\} \]
\[ B=\{(x,y):y=-x,\ x\in R\} \]
then
(a) \(A\cap B=A\)
(b) \(A\cap B=B\)
(c) \(A\cap B=\phi\)
(d) \(A\cup B=A\)
Solution
For intersection,
\[ \frac1x=-x \]
\[ 1=-x^2 \]
\[ x^2=-1 \]
There is no real value of \(x\) satisfying this equation.
Therefore, the two sets have no common element.
Answer
\[ \boxed{A\cap B=\phi} \]
Correct option: (c)