`R = { (a,b), a<= b^2}`

Let A={ (a,b,c} we define R = { (a,b), (b,a), (b,b), (a,a)} then

Which of the following relations R in the set Zof integers is not an equivalence relation? (A) R={(a,b); 3 divides (a - b) (B) R={(a,b); 2 divides (a - b) (C) R= {(a,b): 2 divides (a +b) (D) R = {(a,b): 3 divides (a +b)

Let R be a relation from N to N defined by R = {(a,b) in N and a = b^2} . Are the following true? (a,b)in R , implies (b,a) in R

If Set A= {a, b, c, d} , then a relation R= {(a, b), (b, a), (a, a)} on A is :

Let R be the relation in the set N given by R = {(a,b):|a-b| is odd}. Then:

Let R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)). Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R . Justify your answer in each case.

Let R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)}. Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R . Justify your answer in each case.