The correct options are
A n(P)=54
C n(P ∩ R)=11
D n(P ∪ Q ∪ R)=54
Let logab=t
Then, t2−5t+6=0
(t−2)(t−3)=0
⇒t=2,t=3
⇒b=a2 or b=a3
Case−1:
If b=a2,
then a2≤2020
⇒a≤44
So, ordered pairs (a,b) are of form (a,a2)
{(2,22),(3,32),…,(44,442)}
Number of ordered pairs =43
Case−2:
If b=a3,
then a3≤2020
⇒a≤12
{(2,23),(3,33)⋯(12,123)}
Number of ordered pairs =11
∴n(P)=43+11=54
Since, 2≤b≤2020
Q={(2,22),(3,32),…,(44,442)}
n(P∩Q)=43
and R={(2,23),(3,33),…,(12,123)}
n(P∩R)=11
n(P∪Q∪R)=∑n(P)−∑n(P∩Q)+∑n(P∩Q∩R)
=54+43+11−43−0−11+0
=54