Let A, B, C be 3 sets. If A belongs to B, and B is a subset of C, is it true that A is a subset of C?
They say A is a set. So A should be a subset of C.
But my textbook says it’s not because A is an element (as seen in the belongs to area).
So what is the question trying to say? I’m really confused.
Best Answer
Note: In general, an object can be both a set on its own, and an element of another set.
In your particular case, as J. W. Tanner's question comment indicates, $A$ is an element of $C$ (due to it being an element of $B$ and $B$ being a subset of $C$) regardless of its status of whether or not it is a set on its own.
For $A$ to be a subset of $C$, it must either be empty or contain at least one element of $C$. However, the only specific element of $C$ you are given is $A$ itself, but $A$ doesn't contain itself as an element of its own set.