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

**angrynapkin** · September 8th 2009, 07:09 AM

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

**Plato** · September 8th 2009, 07:19 AM

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?

**angrynapkin** · September 8th 2009, 07:23 AM

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

**Plato** · September 8th 2009, 07:29 AM

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? $\left( {\forall z} \right)\left( {\left[ {x_0 > y_0 \Rightarrow x_0 = z} \right] \wedge \left[ {x_0 \leqslant y_0 \Rightarrow y_0 = z} \right]} \right)$

**angrynapkin** · September 8th 2009, 07:37 AM

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

**Plato** · September 8th 2009, 07:46 AM

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

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