BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

Let S denote the set of all triangles in a plane. Let R be the relation on S defined by ( _1, _2 ) R triangle _1 _2 : (i) Let any triangle S, we have _1 _2 ( , ) R S R is reflexive on (ii) Let _1, _2 ~S , such that ( _1, _2 ) R, then _1 _2 _2 _1 ( _2, _1 ) R R is symmętric (iii) Again, let _1, _2, _3 ~S such that ( _1, _2 ) R and ( _2, _3 ) R _1 _2 _3 ( _1, _2 ) R R is transitive. R is an equivalence relation.