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The relation x² = xy can be described as:

1. both symmetric and reflexive
2. only reflexive
3. reflexive and transitive
4. an equivalence relation

Correct answer: reflexive and transitive

Solution

R={(x,y):x(x-y)=0}, i.e. x=0 or x=y. It is reflexive (x=x always). Not symmetric ((0,5) holds but (5,0) gives 25=0, false). It is transitive (if a=0 then (a,c) holds; if a=b then b=0 or b=c each forces a=0 or a=c). So reflexive and transitive (idx 2); stored 'symmetric and reflexive' is wrong.

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