in the set A = { , , , , , } 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 cm taller than y } (d) R = {( x , y ) : x is wife of y } (e) R = {( x , y ) : x is father of y } . Show that the relation R in the set R of real numbers, defined as R = {( a , b ) : a ≤ b } is neither reflexive nor symmetric nor transitive. . Check whether the relation R defined in the set { , , , , , } as R = {( a , b ) : b = a + } is reflexive, symmetric or transitive.
. Show that the relation R in R defined as R = {( a , b ) : a ≤ b }, is reflexive and transitive but not symmetric. . Check whether the relation R in R defined by R = {( a , b ) : a ≤ b } is reflexive, symmetric or transitive.
. Show that the relation R in the set { , , } given by R = {( , ), ( , )} is symmetric but neither reflexive nor transitive. . Show that the relation R in the set A of all the books in a library of a college, given by R = {( x , y ) : x and y have same number of pages} is an equivalence relation.