# R U S, reflexive (Proof Method)

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• May 20th 2010, 01:07 AM
l flipboi l
R U S, reflexive (Proof Method)
Hello,

Can someone please help me do a proof by contradiction on this problem?

Suppose that r and s are reflexive relations on a set A. Prove or Disprove this statement.

r U s is reflexive

I'm stuck with proof by contradiction (Thinking)
• May 20th 2010, 05:09 AM
Plato
Quote:

Originally Posted by l flipboi l
Suppose that r and s are reflexive relations on a set A. Prove or Disprove this statement.

If $\mathcal{R}$ is a reflexive relation on set $A$ then $\Delta _A \subseteq \mathcal{R}$.
If $\mathcal{S}$ is any other relation on $A$ then
$\Delta _A \subseteq \mathcal{R}\cup \mathcal{S}$ which means the union is reflexive.
• May 20th 2010, 02:11 PM
l flipboi l
Quote:

Originally Posted by Plato
If $\mathcal{R}$ is a reflexive relation on set $A$ then $\Delta _A \subseteq \mathcal{R}$.
If $\mathcal{S}$ is any other relation on $A$ then
$\Delta _A \subseteq \mathcal{R}\cup \mathcal{S}$ which means the union is reflexive.

Thanks! is this direct proof?
• May 20th 2010, 03:51 PM
Plato
Quote:

Originally Posted by l flipboi l
is this direct proof?

That proof is about as direct as it ever gets.
• May 20th 2010, 11:24 PM
l flipboi l
Quote:

Originally Posted by Plato
That proof is about as direct as it ever gets.

Thanks! is there a way to show using proof by contradiction?
• May 21st 2010, 05:50 AM
Plato
Quote:

Originally Posted by l flipboi l
Thanks! is there a way to show using proof by contradiction?

Yes, but then we end up using the very idea I gave you in the so called direct proof.