Let and be a relation on the set defined by . Then the number of elements in is

Question

Let  and  be a relation on the set  defined by . Then the number of elements in  is

Canvas Classes · Accepted Answer

🧠 Fibre-Count: For Each Value of , Multiply LHS-Count by RHS-Count

The relation requires . So for each possible value , count how many  pairs give  and how many  pairs give . Multiply, then sum over .

This is the same fibre-count trick from STRL-010: partition both sides by their condition value, then .

🗺️ Working It Out

Compute  for all  and tally by value:

|  |  |  |  |  |
|---|---|---|---|---|
|  |  | |  |  |
|  |  | |  |  |
|  |  | |  |  |
|  |  | |  |  |
|  |  | |  |  |
|  |  | |  |

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