Let R be a relation from the set 1 , 2 , 3 … … … , 60 to itself such that R = a , b : b = p q , where p , q ≥ 3 are prime numbers . Then, the number of elements in R is

Step-by-step solution

Given b = p q where p   &   q are prime numbers ≥ 3 and 1 ≤ p q ≤ 60 If p = 3 , q = 3 , 5 , 7 , 11 , 13 , 17 , 19 And if p = 5       q = 5 , 7 , 11 and so on, So, b will be 3 × 3 , 3 × 5 , 3 × 7 , 3 × 11 , 3 × 13 , 3 × 17 , 3 × 19 , 5 × 5 , 5 × 7 , 5 × 11 , 7 × 7 i.e. total 11 possibilities Now a can be 1 , 2 , ⋯ , 60 i.e. total 60 possibilities Hence, the number of relations = 60 × 11 = 660