If A=(x,y):y=4x,0≠x∈R and B={(x,y):y=x,x>0,x∈R}

Given,A=(x,y):y=4x,0≠x∈R⇒A is the set of all points on the graph of xy = 4and  B={(x,y):y=x,x>0,x∈R}⇒B is the set of all points on the Graph of y = x, x>0 Now, we plot the graph of given sets.Since' the graph of xy = 4 and y = x, x> 0 intersect at one point.∴A∩B≠ϕ and A∩B is a singleton set.