Hi

I have this problem in the topic of relations.

Suppose is a relation on , and define a relation

on as follows.

for each part ,give either a proof or a counterexample to justify your answer.

a)If is reflexive , must be reflexive ?

I was able to prove this part. I was just playing with the examples which

satisfy the above theorem.

Let

and lets define

clearly is reflexive. So S would be

is correct ? I included since , in the condition for

, we have ,

which can be written as an implication,

so if

then the antecedent is true always , as can be seen from the truth table of the

implication. But I couldn't include the ordered pairs like

in because if we let

and

then is true but is false

Which means that, in the implication , antecedent is true and the consequent is false,

which according to the truth table is false. So

doesn't satisfy the condition for the inclusion in .

is my reasoning correct ? If so, then we can see that is also reflexive,

which is what the above theorem asserts

I see one problem the way symbol for the power set P is displayed. I have used

\mathscr{P} to display slanted P, but it just displays ordinary . Is maths packagemathrsfsinstalled on this forum ?

thanks