Determine whether the relation R in the set A = {1,2,3,4,5,6} as R = {(x,y) : y is divisible by x} is reflexive, symmetric and transitive.

Let R be relation on the set A = {1,2,3,.....,14} by R = {(x,y):3x - y = 0} . Verify R is reflexive symmetric and transitive.

Determine w hether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1,2,3,…,13,14} defined as R = {(x,y): 3x -y =0} (ii) Relation R in the set N of natural numbers defined as R = {(x,y): y = x +5 and x lt 4} (iii) Relation R in the set A ={1,2,3,4,5,6}as R = {(x,y):y is divisible by x} (iv) Relation R in the set Z of allintegers defined as R= {(x, y) : x -y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x,y) : x and y work at the same place} (b) R = {(x,y):x and y live in the same locality] (c ) R ={(x,y) :x is exactly 7 cm taller than y} (d) R = {(x,y) :x is wife of y} (e) R = {(x,y):x is father of y}

Check whether the relation R defined in the set {1,2,3,4,5,6,} as R={(a,b) :b= a+1} is reflexive or symmetric.

Check whether the relation R defined in the set {1,2,3,4,5,6} as R{(a,b): b=a+1)} is reflecxive or symmetric.

Show that the relation R is the set of real numbers R defined as R= {(a, b): a le b^(2) } is neither reflexive, nor symmetric, nor transitive.

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2) ., (2,3)} is reflexive but neither symmetric nor transitive.

If A = {1,2,3} and R = { (1,1}, ( 2,2), (3,3)} then R is reflexive, symmetric or transitive?

If a relation R on the set {1, 2, 3} be defined by R={(1, 1)} , then R is