# proof

• October 21st 2009, 01:01 PM
proof
If A is a subset of B, then A X A is a subset of B X B

hoe do you prove this
• October 21st 2009, 01:14 PM
artvandalay11
Quote:

If A is a subset of B, then A X A is a subset of B X B

hoe do you prove this

$A\subseteq B$ so if $x\in A$ then $x\in B$

A X A= $\{ (x,y) | x,y\in A \}$ but since $x,y\in A$, $x$ and $y \in B$

So all $(x,y)\in B$, so AXA $\subseteq$BXB
• October 28th 2009, 02:35 PM
how do you prove the reverse of that

if A X A subset B X B, then A subset of B
• October 28th 2009, 02:48 PM
Plato
Quote:

how do you prove the reverse of that
if A X A subset B X B, then A subset of B

If $x\in A$ then $(x,x)\in A\times A$. Can you explain that?

Then can you prove that implies that $x\in B?$

How does that prove that $A \subseteq B?$
• October 28th 2009, 03:10 PM
Proof: Assume x is an element of A. (x,x) is therefore an element of A X A because the definition of A X A is the set of (x,x) such that x is an element of A and x is an element of A. Since , A X A is a subset of B X B (x,x) must also be an element of B X B which means X is an element of B and x is an element of B. x is an element of B so A is a subset of B

is this right reasoning
• October 28th 2009, 03:14 PM
Plato
Quote: