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.
5. 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.
a) For all ordered pairs (a, b) in Z × (Z \ {0}), is (a, b) r (a, b)?
b) For all ordered pairs (a, b) and (c, d) in Z × (Z \ {0}), if (a, b) r (c, d), is (c, d) r (a, b) ?
c) For all ordered pairs (a, b), (c, d) and (e, f) in Z × (Z \ {0}), if (a, b) r (c, d) and (c, d) r (e, f), is (a, b) r (e, f)?