2
$\begingroup$

Result: $(A\times C)-(B\times C)\subseteq (A-B)\times C$

Proof: Let $(x,y)\in (A\times C)-(B\times C)$. Then $(x,y)\in A\times C,\implies x\in A,y\in C$. Since $(x,y)\notin B\times C, x\notin B$. Thus $x\in A-B$ and hence $(x,y)\in (A-B)\times C$

  • 1
    Nothing wrong with it. Why do you think there is?2012-10-20
  • 0
    As this is a question which required to evaluate the proposed proof of the result and i am not sure how to do it2012-10-20
  • 0
    Good proof, brief too. Grammatically a bit funny. For example, "Let $X$ $\implies$ $Y$" is non-standard English syntax, understandable but ungrammatical. And some sentences do not end with periods.2012-10-20
  • 0
    And the logic is not entirely clear. Overuse of $\implies$. Also, should separate what $(x,y)\in A\times C$ implies from what $(x,y)\not\in B\times C$ implies.2012-10-20

1 Answers 1