Because these two propositions are existential, as indicated by the word "some," we use the existential quantifier in their translations. Again we begin by noting that they each involve two propositional functions, Sx, and Px. 

Let's begin with "Some S are P."  If you recall the Venn Diagram representation of this proposition, it does indeed assert that there are any things which are S. It says that there is at least one thing which is S and is also P.  In light of this, the correct translation is:

Again, notice that the scope of the quantifier ranges over the rest of the wff. This sentence is not a conjunction, even though it has an ampersand. The main operator is the existential quantifier, if we think of the quantifier as an operator.

Now let's look at "Some S are not P."  Again, it helps to refer back to the Venn Diagram. This sentence also claim that there are S things, and that at least one S thing is not a P thing.  So we have: