## mathmath333 one year ago Set Theory.

1. mathmath333

\large \color{black}{\begin{align}& \normalsize \text{Let }\ A,B\ \text{and }C\ \text{be three sets. } \hspace{.33em}\\~\\ & \normalsize \text{If}\ A\in B\ \text{and}\ B\subset C,\hspace{.33em}\\~\\ & \normalsize \text{Is it true that }\ A\subset C\ ?\hspace{.33em}\\~\\ \end{align}}

2. Loser66

Sure

3. mathmath333

I have to show it with example

4. Michele_Laino

every element of A is also an element of B, and every element of B is also an element of C, so every element of A is an element of C

5. Loser66

|dw:1438616813096:dw|

6. mathmath333

Wait my book says it it false

7. Michele_Laino

also this example works well: |dw:1438616949711:dw|

8. mathmath333

wait let me show my book proof

9. Loser66

wwwwwwwwwwwat?? hahaha,.... then I failed!!

10. mathmath333

11. mathmath333

|dw:1438617127714:dw|

12. Loser66

Yes!! it is perfect. I am sorry for my careless!! $$\in \neq \subset$$

13. freckles

A that little e thing B means A is an element of B and no a set can't be a element of another set it can be a subset of another set

14. Michele_Laino

the same of @Loser66, I'm very sorry @mathmath333

15. Loser66

hihihi.,.... no worry, everybody has mistake.