No P are M.
Some S are not M.
Therefore, Some S are not P.

If you can't see the diagram you can download it from the "Attach Files" from the Additional Options Given Below.

If you see the diagram, the first premise is drawn by overlaping the area of M and P. This id Beacause it says "No P are M". Then they draw the second premise by putting a cross on the curve of P. now this is something I don't
Understand. They say that the conclusion is wrong. May be it's because the cross sign is on the curve. But according to the second premise, we were suppose to draw the cross outsite M-circle and somewhere inside S-circle. Then why have we drawn it right on the curve of P-circle. If we had drawn it a little right to it's actual position (popsition indicated by the red arrow) in the diagram, then the conclusion would have been correct. So, how do we know where the cross has to be drawn.

GB

I'm no expert on this - just like to add an observation if I may!

From the premises that you have declared, the circle for P doesn't need to intercept either of S or M does it? "No p are M" so they don't intercept at all. And there is no premise that states that S has any relation to P either therefore the only circles to intercept are S & M. Please forgive me if I have misunderstood the concept here but it has been about 15 years since I did anything like this.

Here is one possible "arrangement" of S, P and M which shows that the conclusion is wrong.

In the diagram below, No P are M. That means that there can be no part of P in M (I'm referring to S, P and M as mathematical sets, but it's the same with philosophy). Some S are not M. This clearly only says that there is a part of S that is not M. It doesn't say there HAS to be a part of S that IS in M. Only that there is a part of S that's not in M. One possible way is that the whole S is not M. But, since P and M have nothing in common, whole S can be "inside" P. Therefore, "Some S are not P" is incorrect, because we just showed that there is an arrangement of S, P and M for which the conclusion is not correct.

For a conclusion to be correct, there can be no "arrangement" of S, P and M for which the conclusion can be false.