Question

Set Theory.

Answer 1

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

Answer 2

Sure

Answer 3

I have to show it with example

Answer 4

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

Answer 5

Wait my book says it it false

Answer 6

also this example works well:

Answer 7

wait let me show my book proof

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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