- #1

Suraj M

Gold Member

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## Homework Statement

If a relation R on N × N is

(a,b)R(c,d) iff

ad(b+c) = bc(a+d)

## Homework Equations

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## The Attempt at a Solution

I got the reflexive and symmetric parts but not the transitive part...

here's what i have

## (a,b)(c,d)∈R and (c,d)(e,f)∈R##

To prove ##(a,b)(e,f) ∈ R## .i.e., ##af(b+e)= be(a+f)##

i have

$$ad(b+c) = bc(a+d)$$and$$de(c+f) = cf(d+e)$$

my attempt was...

multiplying we get $$afcd(b+c)(d+e) = becd(c+f)(a+d)$$

$$af(b+c)(d+e) = be(c+f)(a+d)$$

by cancelling ##afbe## on both sides i get

$$af(bd+cd+ce) = be(ac+cd+fd)$$

stuck here :(

is this a wrong method, if not how do i proceed??,

Thank you