Cartesian product

**onemore** · March 8th 2010, 10:20 PM

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

**Mimi89** · March 9th 2010, 03:13 AM

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?

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