1

This page from a logic book I am studying argues from a Boolean standpoint that Venn diagram should be made the way it is in the following diagram. My question is how is he putting an 'X' the the region that overlaps S, M and P for the first statement which is Some M are not P. Since the only relation implied here is between M and P and he should put an 'X' there.

2

I think what your author is doing there is writing the X on the line (rather than in the region) in order to show that we're not certain which side of the line it falls on.

The first premise guarantees us that there's an object a that is an M but not a P. Is a also an S? We just don't know, therefore we can't put our X either in the region where S and M overlap, nor can we put it in the region where we don't. We compromise, therefore, and write the X on the line to show we aren't sure.

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