R U S, reflexive (Proof Method)

Sep 2009
181
0
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)
 

Plato

MHF Helper
Aug 2006
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8,633
Suppose that r and s are reflexive relations on a set A. Prove or Disprove this statement.
If \(\displaystyle \mathcal{R}\) is a reflexive relation on set \(\displaystyle A\) then \(\displaystyle \Delta _A \subseteq \mathcal{R}\).
If \(\displaystyle \mathcal{S}\) is any other relation on \(\displaystyle A\) then
\(\displaystyle \Delta _A \subseteq \mathcal{R}\cup \mathcal{S}\) which means the union is reflexive.
 
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Sep 2009
181
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If \(\displaystyle \mathcal{R}\) is a reflexive relation on set \(\displaystyle A\) then \(\displaystyle \Delta _A \subseteq \mathcal{R}\).
If \(\displaystyle \mathcal{S}\) is any other relation on \(\displaystyle A\) then
\(\displaystyle \Delta _A \subseteq \mathcal{R}\cup \mathcal{S}\) which means the union is reflexive.
Thanks! is this direct proof?