Maths · Relations, type of relations, equivalence relations
is a relation (defined on set ) which is
\( x^{2}=x y \) is a relation (defined on set \( R \) ) which is
- A. Symmetric
- B. Reflexive
- C. Transitive
- D. None of these
Step-by-step solution
The relation defined by x^2 = xy simplifies to x(x-y)=0, so (x,y) is in the relation iff x=0 or x=y. This includes (x,x) for all x ∈ R, so the relation is reflexive. It is also transitive but not symmetric.
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