# Is it $(E\land S\land C)\implies L$ or $L\implies(E\land S\land C)$?

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 $$P$$?

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

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