If sets A and B are defined as A={(x,y)|y=1x,x≠0, x ϵ R},B={(x,y)|y=−x, x ϵ R}, then
A∩B=A
A∪B=B
A∩B=ϕ
A∪B=A
x ϵ (A∩B)⇒x ϵ A and x ϵ Bi.e. y=1x and y=−x ∴ x ϵ A∩B ⇒−x=1x ⇒−x2=1 ⇒x2=−1, This is not possible for any real value of x. ∴A∩B=ϕ
If the sets A and B are defined as
A = {(x, y) : y=1x, 0 ≠ x ∈ R}
B = {(x, y) : y = -x, x ∈ R}, then