1
$\begingroup$

I have some questions as follow...

1) How could I prove transitive closure $t(R)=R^+$, where $R^+=\bigcup_{k=1}^{\infty}R^k$, $R\subseteq A\times A$?

2) Prove or disprove: For any subset $A'\subseteq A,$ we always have $A' \subseteq f^{-1}(f(A'))$?

  • 0
    Start by writing down the definitions of transitive closure, and of $f^{-1}(f(A'))$, and try to work from there. (This sounds like pretty obvious advice, but it's surprising how often people don't even do that before deciding they don't know how to approach a problem.)2012-10-20
  • 0
    Thanks! I take your advice and prove it.2012-10-24
  • 0
    What are you stuck on with the first one? Do you know the definition of transitive closure and of $R^k$?2012-10-25

1 Answers 1