<p>Let R = {(a, b) : b = pq, p, q ≥3 prime} from {1, . . . , 60} to itself. The number of elements
in R is:</p>
Step-by-Step Solution
Key Concept: Count distinct valid b values (b = pq \leq60, p, q \geq3 prime). For each b, a can be any of 60 values.
Total = (valid b count) \times 60.
<p><strong>Step 1</strong>: List all products b = pq \leq60 with p \leqq, both primes \geq3:</p><br>p<br>Valid q<br>Products b<br>Count<br>3<br>3,5,7,11,13,17,19<br>9,15,21,33,39,51,57<br>7<br>5<br>5,7,11<br>25,35,55<br>3<br>7<br>7<br>49<br>1<br>\geq11<br>none (112 = 121 > 60)<br>—<br>0<br>Total<br>11<p><strong>Step 2</strong>: For each of the 11 valid b values, a can be any element of {1, . . . , 60}: 60 choices.</p><br>Total = 11 \times 60 = 660.
Correct Answer: 2