Question

If r is a relation on the sets of integers such tha (a,b)=r, if and only if '3a=4b=7n

Answer 1

Answer:

correct the question 3a+4b=7n. thank you

Mark as braniest ♥️♥️♥️

Answer 2

Given that, ≈ on Z by a≈b  if  '3a=4b=7n

(i) $3a+4a=7a,a$Ε$Z$

$a$≈$a$∀$(a,a)$∈$Z$

so ≈ is reflexive

(ii) $3a+4b=7n$

$3b+4a=7a+7b-(3a+4b)$

           $=7a+7b-7n$

          $=7(a+b-n)$

Which is divisable by7 $a$≈$b$ symmetric

(iii) $a$≈$b$ , $b$≈$c$

as $a$≈$b$ , $3a+4b=7n,n$∈ $Z$ ---eqno:1

   $b$≈$c$ , $3b+4c = 7m$ , $m$ ∈ $Z$--eqno:2

From both 1 and 2 ewquation,

$3a+4b+3b+4c=7m+7n$

     $3a+4c=7m+7n-7b$

    $3a+4c=7(m+n-b)$ which is divisable by 7

hence,≈ satisfies reflexive symmetry & transitive relation.