How many reflexive relation are there on a set with n elements ?
2026-03-29 15:41:34.1774798894
How many reflexive relation are there on a set with n elements?
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Let $A$ be this set. Write $A\times A$ in a grid. If the square $(j,k)$ is marked, that means that $jRk$.
Since the relation is reflexive you must mark the main diagonal. They are $n$ squares. Now the question is: 'How many ways are there to mark or not the other squares of the grid?'. There are $n^2-n$ squares, and there are $2$ possibilities for each. Then, there are $$2^{n^2-n}$$ possibilities.