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Text book: "1. Symbolize each statement using the suggested notation. a) (bumper sticker) "Sometimes I Wake Up Grumpy, And Sometimes I Let Him Sleep." (W= Sometimes I wake up Grumpy, S= Sometimes I let Grumpy sleep."" That is straight from my textbook. As of right now I think they are two separate statements. I know (think) this is not an "if-then"/"Arrow In" situation. I don't know if I need to actually put the "and" sign in. What symbol (if any) should I use?

W, S OR W & S

Thank you!

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    The use of the term "sometimes" suggests quantification. The given statement can't be adequately represented in propositional calculus, you need predicate calculus. **Edit:** Or maybe [temporal logic](https://en.wikipedia.org/wiki/Temporal_logic). – 2017-01-24
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    @GitGud I'm very confused by this question because it is straight out of a propositional logic book! So, as I understand it, these are two totally unrelated ideas to be separated by a comma? Thank you for the quick answer! – 2017-01-24
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    For reference, what book is this? Imagine propositional calculus with a twist: the only connective is *and*. It's not hard to convince oneself that such a logic has very limited expressive power. By the same token (full) propositional logic isn't enough to model everything we assert in a natural language (like English). The statement in your question, I claim, is one such instance in which propositional calculus isn't enough. If the book claims it is possible to model this in propositional calculus, then I say the authors are wrong. **Edit:** What I said is assuming that W and S are as you say – 2017-01-24
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    @GitGud thank you. The book is "introduction to logic propositional logic revised third edition by Howard pospesel" – 2017-01-24
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    Please note the edit to my previous comment. Who provided $W$ and $S$, you or the author? – 2017-01-24
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    The book told me everything. I'll edit the original post to be more exact – 2017-01-24
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    Post question edit: this is very different as "sometimes" is now incorporated in both $W$ and $S$. OK, back to the question. The book probably defined what symbol, stands in for *and*. The most common one is $\land$. Sometimes $\&$ is used. This should be explicitly mentioned in the book. – 2017-01-24
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    "And" is the ampersand "&" so it will be needed? – 2017-01-24
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    Yes, it will be needed. Care to try for an answer? – 2017-01-24
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    @GitGud yes thank you so much! (This is why math is not my friend....) so it would be. 1) W & S proof is assumed 2) W proof with "1) & out" and 3) S proof with "2,1 & out". something like that? – 2017-01-24
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    The answer is just $W\& S$, the rest that you mentioned, I simply don't understand. – 2017-01-24
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    @GitGud yeah. Doesn't make sense to me either. I'm glad that about that. I'm probably over thinking. Thank you :) – 2017-01-24
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    You're welcome. Good job $\ddot \smile$ – 2017-01-25

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