a ~ b Relations

I am really struddling to understand these types of questions. Please can someone walkthough it with me.

The Question is

On the set N, define a relation ~ by stipulating that a ~ b if
hcf(a,b) = 1 (where a; b 2 belong to N). Decide if this relation is (a) reflexive, (b) symmetric and
(c) transitive, in each case giving either a proof or a counterexample, as appropriate.

Any help would be great thanks

I think i have managed to do part (a)
if a~a then hcf(a,a) = a. If a =1,2,3,4,5.... the hcf(a,a)=1,2,3,4,5... Not 1 for all cases. Therefore not reflexive

Quote:

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Originally Posted by Matt1993

The Question is
On the set N, define a relation ~ by stipulating that a ~ b if
hcf(a,b) = 1 (where a; b 2 belong to N). Decide if this relation is (a) reflexive, (b) symmetric and (c) transitive, in each case giving either a proof or a counterexample, as appropriate.

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You know that
so what does that tell you about transitivity?

that its not transative because hcf(8,9)=1 and hcf(9,10)=1 but hcf(8,10)= 2

Quote:

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Originally Posted by Matt1993

that its not transative because hcf(8,9)=1 and hcf(9,10)=1 but hcf(8,10)= 2

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That is correct. The relation is symmetric. WHY?

is it because hcf(a,b) = hcf(b,a) = 1. a and b are both still coprime