# Is this symbolic expresson correct?

Hello. I'd like to check my answer for 1. (g)

$\forall$ x $\in$ A, P(x), $\forall$ y $\in$ A, C(y) $\wedge$ F(y), $\forall$ z $\in$A, C(z), T(x, y) $\implies$ T(x, z)

Is this correct?

Thank you

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What does the comma in your notation mean? – dtldarek Oct 19 '13 at 21:11
To separate the domain and predicates? Are you not supposed to use commas? – muros Oct 19 '13 at 21:19
Not the commas after $\in A$, but those before $\forall$-s, or the one between $C(z)$ and $T(x,y)$. – dtldarek Oct 19 '13 at 22:05

I'd suggest the use of parentheses to help disambiguate the scope of each quantified variable, replacing some of the commas. You also need a connective following $C(z)$. Here is my suggested translation:

"If any professor has taught every first-year course, then that professor has taught every course."

$$\forall x \in A, \Big(\{P(x) \land \forall y \in A, [(C(y)\land F(y)) \rightarrow T(x, y)]\}\rightarrow \forall z \in A, (C(z) \rightarrow T(x,z))\Big)$$