Determine whether Relation `R` on the set `A={1,\ 2,\ 3,\ ,\ 13 ,\ 14}` defined as `R={(x ,\ y):3x-y=0}`

Determine whether Relation R on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6} defined as R={(x ,\ y): y is divisible by x} is reflexive, symmetric or transitive.

Determine whether 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 all integers 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 }

Determine whether Relation R on the set N of all natural numbers defined as R={(x ,\ y): y=x+5 and x<4} is reflexive, symmetric or transitive.

Determine whether Relation R on the set Z of all integer defined as R={(x,y):y is divisible by x}

In the set A={1,2,3,4,5}, a relation R is defined by R={(x,y)x,y in A and x

Write the following relations as the sets of ordered pair: A relation R on the set {1,2,3,4,5,6,7} defined by (x,y)in R hArr x is relatively prime to y .

If the relation R : A to B, where A={1,2,3} and B={1,3,5} is defined by R= {(x,y):xlty,x in A,y in B}, then-

The relation R defined on the set A = {1,2,3,4, 5} by R ={(x, y)} : |x^(2) -y^(2) | lt 16 } is given by

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is