Given: A=1,2,3,...20, {R}_{1}={(a,b):b is divisible by a} and {R}_{2}={(a,b):a is an integral multiple of b}.
⇒R1=(1,1),(1,2),...,(1,20),(2,2),(2,4),...,(2,20),(3,3),(3,6),...,(3,18),(4,4),(4,8),...,(4,20),(5,5),(5,10),...,(5,20),(6,6),(6,18),...,(6,18),(7,7),(7,14),(8,8),(8,16),(9,9),(9,18),(10,10),(10,20),(11,11),...,(20,20)
⇒n(R1)=20+10+6+5+4+3+2+2+2+2+10=66
⇒R1∩R2=(1,1),(2,2),(3,3),(4,4),...,(20,20)
⇒n(R1∩R2)=20
⇒n(R1−R2)=n(R1)−n(R1∩R2)
⇒n(R1−R2)=66−20
⇒n(R1−R2)=46