# Predicate Logic -- Can you word this expression in English?

• September 8th 2009, 08:09 AM
angrynapkin
Predicate Logic -- Can you word this expression in English?
I'm pretty sure I can solve the other parts of this problem set if you all can just word out this expression for me:

(x0 > y0 → z = x0) o (x0 <= y0 → z = y0)

The quantifier in the middle throws off my wording
• September 8th 2009, 08:19 AM
Plato
Quote:

Originally Posted by angrynapkin
I'm pretty sure I can solve the other parts of this problem set if you all can just word out this expression for me:
(x0 > y0 → z = x0) o (x0 <= y0 → z = y0)
The quantifier in the middle throws off my wording

I have absolutely no idea how to read that.
Is this close?
$\left[ {x_0 > y_0 \Rightarrow x_0 = z} \right]~{\color{red}{?}}~\left[ {x_0 \leqslant y_0 \Rightarrow y_0 = z} \right]$

But what in the world does ? stand for?
• September 8th 2009, 08:23 AM
angrynapkin
It's the Universal quantifier. Some schools use the upside down A, we use the ^ symbol as well.
• September 8th 2009, 08:29 AM
Plato
Quote:

Originally Posted by angrynapkin
It's the Universal quantifier. Some schools use the upside down A, we use the ^ symbol as well.

Is this it? $\left( {\forall z} \right)\left( {\left[ {x_0 > y_0 \Rightarrow x_0 = z} \right] \wedge \left[ {x_0 \leqslant y_0 \Rightarrow y_0 = z} \right]} \right)$
• September 8th 2009, 08:37 AM
angrynapkin
Right. Well that's the symbol at least. I just need to figure out what the function actually does.
• September 8th 2009, 08:46 AM
Plato
Quote:

Originally Posted by angrynapkin
Right. Well that's the symbol at least. I just need to figure out what the function actually does.

That is $\max \left\{ {x_0 ,y_0 } \right\}$.