Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C? Please elaborate the solution for the problem. I am not clear with...

``Hello!

I think you mean  `A sub B` and `B sub C.` Yes, this implies that `A sub C.` Let's prove.

A set `A sub B` means by definition that any element `a in A` is also ` in B.`  `B sub C,` in turn, means that any `b in B` is also `in C.`

Now whether  `A sub C?`  Any ` a in A` is also `in B` because `A sub B.` `a in B` implies `a in C` because `B sub C.` This way we proved that any `a in A` is also `in C,` so by definition  `A sub C.`