1.

Determine whether each of the following relations is reflexive, symmetric and transitive.Relation R in the set A of human beings in a town at a particular time given by R={(x,y): x is father of y }

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SOLUTION :Clearly (X,x)`!in`R for any `x in A`
`THEREFORE`R is not reflexive `(x ,y) inR RARR ` x is FATHER of y
`rArr `y can.t be father of x
`rArr (y,x)!in R`
`therefore `R is not symmetric `(x,y) in R (y,z)in R `
`rArr ` x is father of y and y is father of z
`rArr` x can.t be father of z(br)`rArr (x,z) !in R`
`therefore`R is not transitive .


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