Can someone explain how answer E was concluded ?

Hi @pmornelasperez@ucdavis.edu, Thanks for the question! So I’ll reproduce the diagram real quickly (sorry if my notation doesn’t match up with the video): SC = small country SH = southern hemisphere (country) PSUNSC = permanent seat on UNSC IIPE = (in favor of) increased international peacekeeping efforts GRUN = (in favor of) greater role for UN in moderating regional disputes) AISRUN = (against increased spending on refugees by UN) SC v SH —> ~PSUNSC PSUNSC —> IIPE & GRUN IIPE <—some—> AISRUN So now you’re question is essentially, how do we get from PSUNSC —> IIPE & GRUN to GRUN <—some—> ~SH (which is the correct answer choice). Well, first, what we need to do is get from GRUN <—some—> PSUNSC which we can do from the conditional PSUNSC —> IIPE & GRUN and we can think this through with an example. For example, let’s say that all avocados are fruit. Avocado —> Fruit Well, if we know this, and we know that avocados exist (which we do), then we also know that some fruit are avocados, right? Because avocados exist, and they’re fruit, so of course some fruit have to be avocados! So in general, when we have A —> B, and we know that A exists, we can conclude that some Bs are As. Here, we can apply that to get that ??IIPE & GRUN <—some—> PSUNSC And of course, if some things that are IIPE and GRUN are PSUNSC, then some things that are GRUN are PSUNSC as well (since the first is a subset of the second). So now we know that ??GRUN <—some—> PSUNSC And we can then take the contrapositive of the first statement to get PSUNSC —> ~SC & ~SH Which we can chain to that to get GRUN <—some—> PSUNSC —> ~SC & ~SH which we can simplify to GRUN <—some—> ~SH??And that’s how we get to (E). Hope this helps! Feel free to ask any other questions that you might have.

Hello, thank you for explaining this to me. I'm still confused on why convert PSUNSC —> IIPE & GRUN to a some statement. I understood your reasoning but I didn't know that was a rule we could use. Essentially could we convert any S &N statement into a Some statement? My other question was if you needed to reverse it, why not reverse and negate instead of turning it into a Some statement?

We can convert any S&N into a some statement provided we know that the sufficient condition holds/exists. For example, we can't say that some mammals are unicorns because all unicorns are mammals, because unicorns don't exist. And if you mean reverse and negate, we do also take the contrapositive, but for the purposes of this question, we need the some statement.