# Syntax of First-Order Predicate Logic

• May 12th 2010, 04:43 PM
McTaggStar
Syntax of First-Order Predicate Logic
It seems like a trivial question, but does changing the order of the variables within parentheses in a quantified wff change the meaning or truth value? For example:

∀\$\displaystyle x\$∃\$\displaystyle y\$ \$\displaystyle P\$(\$\displaystyle x\$, \$\displaystyle y\$) VS. ∀\$\displaystyle x\$∃\$\displaystyle y\$ \$\displaystyle P\$(\$\displaystyle y\$, \$\displaystyle x\$)

From what I gathered on my own, I didn't think this slight change made a difference to the wff, but I want to be sure to avoid making any sort of mistake. Thanks! (Nerd)
• May 12th 2010, 05:06 PM
hmmmm
yes this change could make a difference if for example P(x,y) meant that x loves y the P(y,x) would mean that y loves x which are different statments,

if however P was the identity relation then clearly x=y is the same as y=x however this being a special case in genral this does make a difference,
hope that helps