Does $\displaystyle X\subseteq Y$ logically imply xεX and xεY ??

Printable View

- Jun 13th 2011, 02:22 PMalexandroslogical implication
Does $\displaystyle X\subseteq Y$ logically imply xεX and xεY ??

- Jun 13th 2011, 02:29 PMPlatoRe: logical implication
- Jun 13th 2011, 02:45 PMemakarovRe: logical implication
I would even start by saying that x has not been defined...

- Jun 13th 2011, 03:42 PMalexandrosRe: logical implication
Yes i agree with both of you,but how do you show that to somebody who insists otherwise??

- Jun 13th 2011, 04:01 PMPlatoRe: logical implication
In this matter I absolutely agree with emakarov's reply.

$\displaystyle \left( {X \subseteq Y} \right) \Leftrightarrow \left( {\forall x} \right)\left[ {x \in X \to x \in Y} \right]$.

Ask your protagonists does imply that $\displaystyle \left( {\forall x} \right)\left[ {x \in X \wedge x \in Y} \right]$ - Jun 13th 2011, 04:09 PMalexandrosRe: logical implication
O.k Thanks we carry on tomorrow