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kenmcfa
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Please be nice to me, I'm new here. Anyway, help to solve this maths problem would be much appreciated:
Work out a detailed proof (below) that the relation on the integers defined by p~q if and only if 7|p-q is an equivalence relation:
a) the relation is reflexive
b) the relation is symmetric
c) the relation is transitive
p~q if and only if 7|p-q
a) (I'm pretty sure this is done right)
If relation is reflexive then:
x[tex]\in[/tex]S[tex]\rightarrow[/tex] (x,x) [tex]\in[/tex]R
Therefore x~x
7|x-x since x-x=0 and 7|0
Therefore relation is reflexive.
That's the easy bit. Now:
b)If relation is symmetric then:
x~y [tex]\leftrightarrow[/tex] y~x
And I don't know how to go on from there. Please help me!
Homework Statement
Work out a detailed proof (below) that the relation on the integers defined by p~q if and only if 7|p-q is an equivalence relation:
a) the relation is reflexive
b) the relation is symmetric
c) the relation is transitive
Homework Equations
p~q if and only if 7|p-q
The Attempt at a Solution
a) (I'm pretty sure this is done right)
If relation is reflexive then:
x[tex]\in[/tex]S[tex]\rightarrow[/tex] (x,x) [tex]\in[/tex]R
Therefore x~x
7|x-x since x-x=0 and 7|0
Therefore relation is reflexive.
That's the easy bit. Now:
b)If relation is symmetric then:
x~y [tex]\leftrightarrow[/tex] y~x
And I don't know how to go on from there. Please help me!
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