3. Recall that for a relation to be an equivalence relation, it must be reflexive, symmetric and transitive. For a relation to be a partial order relation, it must be reflexive, antisymmetric and transitive.
a) Reflexive: For every integer x, is x·x 
1?
Symmetric: For all integers x and y, if x·y 1, does this imply that y·x 1?
Antisymmetric: For all distinct integers x and y, if x·y 1, does this imply that y·x cannot be greater than or equal
to1?
Transitive: For all integers x, y and z, if x·y 1 and y·z 1, does this imply that x·z 1?
b) Reflexive: For every positive integer x, is x a multiple of x?
Symmetric: For all positive integers x and y, if x is a multiple of y, does this imply
that y is a multiple of x?
Antisymmetric: For all distinct positive integers x and y, if x is a multiple of y, does
this imply that y cannot be a multiple of x?
Transitive: For all positive integers x, y and z, if x is a multiple of y and y is a
multiple of z, does this imply that x is a multiple of z?
c) Reflexive: For every integer x, is x
x (mod 13)?
Symmetric: For all integers x and y, if xy (mod 13), does this imply that yx (mod 13)?
Antisymmetric: For all distinct integers x and y, if xy (mod 13), does this imply that y cannot be congruent to x
(mod 13)?
Transitive: For all integers x, y and z, if xy (mod 13) and yz (mod 13), does this imply that xz (mod 13)?