How many reflexive relations are there on a set with 4 elements?

Solution: Count reflexive relations by fixing diagonal pairs and choosing the rest.

• There are 4 elements, so total ordered pairs are 4 × 4 = 16.

• A reflexive relation must include the 4 diagonal pairs (one for each element), so those are fixed.

• The remaining ordered pairs are 16 − 4 = 12, and each may be present or absent independently, giving 2^12 possibilities.

• Therefore, the number of reflexive relations is 2^12 = 4096.