# Math Help - Cartesian product

1. ## Cartesian product

Prove: If $A \subset C$ and $B \subset D$, then $A \times B \subset C \times D$.

2. Originally Posted by onemore
Prove: If $A \subset C$ and $B \subset D$, then $A \times B \subset C \times D$.
Note that $A \times B = \{ (a,b) : a \in A, b \in B \}$ and $C \times D = \{ (c,d) : c \in C, d \in D \}$

So, pick an element in $A \times B$, say (a,b). You want to show that it is in $C \times D$.

Now, as $a \in A \subset C$, we have that $a \in C$

Can you take it from here?