Is congruent to" on the set of all triangles is an equivalence relation
Is congruent to" on the set of all triangles is an equivalence relation
The correct option is A True
If we want to check if a given relation is equivalent, we have to see if it is reflexive, symmetric and transitive.
Any given triangle is congruent to itself. => It is reflexive
If a triangle A is congruent to B, then B will also be congruent to A. This implies if aRb, then bRa, which is the condition for the relation to be symmetric.
If triangle A is congruent to B and B is in turn congruent to C, then we can say A is also congruent to C. From a relation point of view this is same as saying if (a,b) and (b,c) are part of the relation, then (a,c) is also part of the relation, which makes it transitive.
Since the given relation, is congruent to, is reflexive, symmetric and transitive, we can say that it is an equivalence relation.
True
If we want to check if a given relation is equivalent, we have to see if it is reflexive, symmetric and transitive.
Any given triangle is congruent to itself. => It is reflexive
If a triangle A is congruent to B, then B will also be congruent to A. This implies if aRb, then bRa, which is the condition for the relation to be symmetric.
If triangle A is congruent to B and B is in turn congruent to C, then we can say A is also congruent to C. From a relation point of view this is same as saying if (a,b) and (b,c) are part of the relation, then (a,c) is also part of the relation, which makes it transitive.
Since the given relation, is congruent to, is reflexive, symmetric and transitive, we can say that it is an equivalence relation.
