Question

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

Answer 1

Let $x\in A.$ Since $A\subseteq B,$ we conclude that $x\in B.$ Taking into account that $B\subseteq C,$ we conclude that $x\in C.$ Therefore, $A\subseteq C.$