To check if a relation R on a set A of four elements has these properties, you'd verify: reflexivity by confirming (a,a) ∈ R for all a ∈ A; symmetry by ensuring if (a,b) ∈ R then (b,a) ∈ R; transitivity by checking if (a,b) and (b,c) ∈ R, then (a,c) ∈ R. In my research on equivalence relations in clustering algorithms, I implement these checks programmatically for validation, which is far more efficient than manual inspection for large datasets. Frankly, the textbook exercise of doing this by hand for four elements feels like making vindaloo with just one chili—a theoretical exercise missing the practical heat of scale.
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