Because these two propositions are universal, we'll use the universal quantifier in their translations. But we begin by noting that they each involve two propositional functions, Sx, and Px. 

Let's begin with "All S are P."  If you recall the Venn Diagram representation of this proposition, it does not assert that there are any things which are S. Rather, it states that if anything is an S, then it is also a P. In light of this, the correct translation is:

Notice that the scope of the universal quantifier ranges over the rest of the wff. This sentence is not a conditional, even though it has a horseshoe. The main operator is the universal quantifier, if we think of the quantifier as an operator.

Now let's look at "No S are P."  Again, it helps to refer back to the Venn Diagram. This sentence also does not claim that there are any S or P things. Rather, it states that if anything is an S, it is not a P.  So: