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

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Q. Let $R$ be a relation from the set $\{1,2$, $3 . \ldots \ldots \ldots, 60\}$ to itself such that $R =\{( a , b ): b = pq$, where $p , q \geq 3$ are prime numbers \}. Then, the number of elements in $R$ is :

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Solution:

Number of possible values of $a=60$, for $b=$ pq,
If $p =3, q =3,5,7,11,13,17,19$
If $p =5 q =5,7,11$
If $p =7 q =7$
Total cases $=60 \times 11=660$