reflexive if, and only if, for
all x
A, x R x.
symmetric if, and only if, for
all x, yA, if x R y
then y R x.
transitive if, and only if, for
all x, y, zA, if x R y
and y R z then x R z.
2.Recall that a relation R on a set A is :
reflexive if, and only if, for
all xA, x R x.
symmetric if, and only if, for
all x, yA, if x R y
then y R x.
transitive if, and only if, for
all x, y, zA, if x R y
and y R z then x R z.
i) For all positive integers a, does a | a?
ii) For all positive integers a and b, if a | b, does b | a?
iii) For all positive integers a, b and c, if a | b and b | c, does a | c?