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14.2 Master Plan: Main Connective

By now you’ve memorized the rules and done many proofs. Next, we’re going to start doing some harder ones.

If you find that the rest of this chapter and the next chapter are harder, don’t worry. You are not alone!

The material starts to get more difficult with Chapters 14 and 15. Now is the time to put in the effort!

The class starts to get more difficult with Chapters 14 and 15. The good news is that it’s not too late to double down on your efforts and seek as much help as you need.

Now is the time to put in more work, not when you’re worried about the midterm or final exam you are about to take!

The fundamental strategy: look at the main connectives.

Now let’s get to the master strategy.

After teaching this material to thousands of students, we’ve distilled our advice down to one key idea: look at the main connectives.

Why the main connectives? Simple: because the Intro and Elim rules only apply to the main connective of a sentence.

Sometimes students see a sentence like this:

~~P&~~Q

And they want to do ~Elim. But they can’t because the sentence is a conjunction. Or they see:

~(PvQ)

And they want to do vElim, but they can’t because the sentence is a negation!

That is why the skill of identifying a sentence’s main connective is so important.

That is why the skill of identifying a sentence’s main connective is so important. You can’t even begin to learn to do harder proofs if you can’t focus on the main connective, and you can’t focus on the main connective if you can’t even find it!

Now that you know to focus on the main connectives, we’ll start talking about what you do with them.