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Mathematics
Problem
Define a relation
R
R
R
on the set of integers
Z
\mathbb Z
Z
by
a
R
b
⟺
a
−
b
is divisible by
5.
a \thinspace R \thinspace b \iff a-b \text{ is divisible by }5.
a
R
b
⟺
a
−
b
is divisible by
5.
Prove, with reasons, whether
R
R
R
is reflexive, symmetric and transitive. Conclude whether
R
R
R
is an equivalence relation.
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