If R is an equivalence relation on a set A, then `R^-1` is A. reflexive only B. symmetric but not transitive C. equivalence D. None of these

Define a relation R on the set A ={a,b,c} which is neither reflexive nor symmetric and transitive.

Let R and S be two equivalence relations on a set A Then : A. R uu S is an equvalence relation on A B. R nn S is an equirvalenee relation on A C. R - S is an equivalence relation on A D. None of these

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a\ R\ b if a is congruent to b for all a ,\ b in T . Then, R is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a\ R\ b if a is congruent to b for all a ,\ b in T . Then, R is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

Let R and S be two equivalence relations on a set A Then : " " A. R uu S is an equvalence relation on A " " B. R nn S is an equirvalence relation on A " " C. R - S is an equivalence relation on A " " D. None of these

If R and R' are symmetric relations (not disjoint) on a set A ,then the relation R uu R' is (i) Reflexive (ii) Symmetric (ii) Transitive (iv) none of these

Statement-1: If R is an equivalence relation on a set A, then R^(-1) is also an equivalence relation. Statement-2: R = R^(-1) iff R is a symmetric relation.

Statement-1: If R is an equivalence relation on a set A, then R^(-1) is also an equivalence relation. Statement-2: R = R^(-1) iff R is a symmetric relation.

Consider that the set A = {a, b, c} . Give an example of a relation R on A. Which is : (i)reflexive and symmetric but not transitive (ii) symmetric and transitive but not reflexive (iii) reflexive and transitive but not symmetric.

Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (2,\ 3),\ (1,\ 3)} be a relation on A . Then, R is (a)neither reflexive nor transitive (b)neither symmetric nor transitive (c) transitive (d) none of these