Question

vritely 2. Let A = {0, 1, 2, 3, 4) and define a relation R on A by Ry iff (x + y) E A. Determine whether R is each of the fol

I'm confused on what it means to be each one. I can't seem to get them straight or fully understand what each means.
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Answer #1

Doubt in this then comment below...i will explain you..

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a) reflexive..

in this we can check for all elemnts a of R , (a,a) belongs to R or not..  

As we see 3+3 = 6 , that does not in A.. so (3,3) not in R ..

So this is not reflexive..

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b) ..

It states that if aRb then bRb or not...

If aRb ..then a+b is in A ...so it is obvious b+a is in A...therefore bRa ..

So this is symmetric ...

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c) .. it states if aRb , and bRc.. then aRc or not....

Here 3R0 and 0R4 ...but (3,4) not in R ...so this is not transitive..

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d) .. this states that if xRy ..then y not related with x ...

But as we do in part b ) .. xRy then yRx also true...

So this is not antisymmetric...

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