The correct options are
A {(2,2),(3,3)}
B {(3,2),(4,2),(4,3)}
D {(1,5),(3,3),(4,2)}
A={x:x is a prime factor of 30}
Prime factors of 30 are 2,3,5
A={2,3,5}
B={y:y∈N,−3≤y+3<8}
−3≤y+3<8
⇒−6≤y<5
Since y∈N
B={1,2,3,4}
B×A={(1,2),(1,3),(1,5),(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(4,2),(4,3),(4,5)}
Here, R is a relation from A to B, then
R−1 is a relation from B to A
Now, {(2,2),(3,3)}⊂B×A
{(3,2),(4,2),(4,3)}⊂B×A
{(2,1),(3,1),(5,2)}⊄B×A
{(1,5),(3,3),(4,2)}⊂B×A