# Can someone explain why this immediate inference is valid?

everyone.

I'm enrolled in an Introduction to Logic course, and we're currently working on Categorical Propositions. I've run into a problem that's baffling me, and I was hoping I might get some help with it.

The instructions for the problem are the following:

Translate the premise and conclusion of the following immediate inferences into standard form categorical propositions. Then use conversion, obversion, contraposition, or the traditional square of opposition to determine whether each is valid or invalid.

The problem with which I'm having trouble is this one:

Flu vaccines are never completely effective. Therefore, not ever flu vaccine is completely effective.

This is one of the exercises for which an answer is provided at the back of the book. The answer provided is this:

No flu vaccines are completely effective medicines. Therefore, some flu vaccines are not completely effective medicines. Valid.

While I think I can understand the rationales for converting the two statements into categorical propositions, I'm having a lot of trouble figuring out how the immediate inference formed from the propositions can be valid.

We have learned by this point about conversion, obversion, and contraposition, and while I think I understand these means of converting the propositions into equivalent statements, none of them (as I understand it, anyway) will work to convert a universal proposition into a particular one.

So, I'm stuck here. There's obviously something I'm missing, but I can't figure out what it is. Any guidance you might be able to offer would be much appreciated.

• We have learned by this point about conversion, obversion, and contraposition, and while I think I understand these means of converting the propositions into equivalent statements, none of them (as I understand it, anyway) will work to convert a universal proposition into a particular one. The question you quoted also tells you that you might need to use "the traditional square of opposition", have you looked into that? Jul 10 at 11:32
• No flu vaccines are completely effective medicines. Therefore, some flu vaccines are not completely effective medicines. Valid. Do you understand this in words? No vaccine is completely effective. What is meant by this? Jul 10 at 15:20
• No are completely is equivalent to some (or all) are not completely. The meaning of completely has changed though. Jul 10 at 15:27