The biggest barrier between me and logic appears to be language. Another question asks How to say "Not only but also", and presents a convoluted English sentence that can be restated as:

$$\text{To do $L$ we have to do $E$, $S$ and $C$}.$$

I assume this can be changed in to an if-then sentence and written as either $(E\land S\land C)\implies L$ or $L\implies(E\land S\land C)$ I can just as easily say that my question is about $P \implies Q$ or $Q \implies P$. This makes a simpler view of my issue. There are many ways to express a relationship between two atomic statements in English:

$$\text{To do $P$ we have to do $Q$}.$$

$$\text{To do $P$ first do $Q$}.$$

$$\text{$Q$ is complete, now do $P$}.$$

$$\text{$Q$ comes before $P$}.$$

$$\text{First $Q$ then $P$}.$$

All of these imply a sequence of first $Q$, then $P$. The logic statement is separated from the sequence of $Q$ then $P$ but appears to present just the opposite sequence. That is, $P \implies Q$ implies $P$ before $Q$.

If the English sentence uses anything other than the an if-then structure and, perhaps specifically those words, how do I determine which one to use, $P$ to $Q$ or $Q$ to $P$?

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    $\begingroup$ @manooooh Thank you for the edit. My question reads much easier now. $\endgroup$
    – user756686
    Commented Mar 14, 2020 at 18:12

1 Answer 1


$L$ requires $E$ and $S$ and $C$, so the truth of $L$ implies that $E$ and $S$ and $C$ are all true: $L\implies E\land S\land C$.


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