gate Discrete

Question

Let A = {1,2,3,4} and let S= A x A .

Define the Relation R on S as(a,b) R (c,d) iff a+b=c+d.

Show that R is an Equivalence Relation and find S/R.

Answer 1

A = {1,2,3,4}

We have to satisfy (a,b) R (c,d) iff a+b=c+d.

for reflexive relation (1,2)R(1,2) satisfies a+b=a+b , Similarly other elements also satisfies reflexivity

for symmetric relation (1,4)R(2,3)=(2,3)R(1,4), So it satisfies symmetric

for transitive relation , no such element exists. So, it satisfies transitivity also.

So,it satisfies equivalence relation

Comments

no it doesnot contain any element like (1,2,3,4)

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A*A===>{(1,1)(1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4) } R ==>(1,1)(2,2)(3,3)(4,4)(2,3)(3,2) (4,1)(1,4) only these elements satisfy...the relation...now on these u check..all the properties..like reflexive...etc

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@Tauhin. Even I didnt get what is S/R. What do you mean by relation algebra? Plz explain.