Question

Show that
If $A\subset C$ then $A\times B\subset C\times B.$

Answer 1

We have
$(x,y)\in A\times B\Rightarrow x\in A$ and $y\in B$
$\Rightarrow x\in C$ and $y\in B$ $[\because A\subset C\therefore x\in A\to x\in C]$
$\Rightarrow (x,y)\in C\times B.$
Hence $A\times B\subset C\times B.$