Let `A={2,3,5}" and relataion "R={(2,5)}` write down the minimum number of ordered pairs to be indluded to R to make it an equivalence relation.

Let A = { a,b,c }, and R = {(a,a) (b,b) (a,c) }. Write down the minimum number of ordered pairs to be included to R to make it (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence.

Let A={a,b,c} and R={(a,a), (b,b),(a,c)}. Write down the minimum number of ordered pairs to be included to R to make it (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence

Let X = {a, b,c,d}, and R = { (a,a) (b,b) (a,c)}. Write down the minimum number of ordered pairs to be included to R to make it (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence.

Let set A={1,2,3} . Then find number of ordered pairs which when added to R make it reflexive but not symmetric

Let A ={1,2,3,4,5,6} . Define a relation R from A to A by R = {(x,y):y =x+1} write down the domain , and range of R .

In the set of integers Z, define mRn if m-n is a multiple of 5. Is R equivalence relation"?

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation