I'm not sure I have these concepts down well enough. The following is a problem from my professor:
Let S = {1,2,3,4,5}. On P(S) define the relation
as follows: A
B iff A
B =
. Is
reflexive? Is
symmetric? Is
transitive?
Since there are elements in P(S) that do not equal
when intersecting themself then
is not reflexive.
If A
B is empty then B
A is empty so
is symmetric.
{1,2}
{3,4} is empty. And {3,4}
{2,5} is empty. But {1,2}
{2,5} = {2}. So
is not transitive.
Is the above correct? If not please explain where I've gone wrong.
Happy KwanzHanukmas!