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11.2 &Intro

Every symbol in BOOL has two rules: Intro and Elim. You’ve already learned how to use or eliminate a conjunction with &Elim.

Now we’ll learn how to use &Intro to make or “introduce” a conjunction.

Here’s a simple example:

1. P
2. Q
3. P&Q

Premise
Premise
&Intro;1,2

Conjunction always requires two sentences, so the rule &Intro must cite two lines.

The rule allows you to put together the conjuncts in whatever order you want. For example, like this:

1. P
2. Q
3. Q&P

Premise
Premise
&Intro;1,2

When you cite the steps, use numerical order. Some logical systems require you to cite the steps in the order that they get conjoined. That would require you to write &Intro;2,1 here, since the Q is conjoined first and it comes from line 2.

Logical systems are tools that can be designed in many ways. Our system uses numerical order for line citations.

But remember, logical systems are tools that can be designed in many ways, and our system uses numerical order for line citations.

It’s your turn to practice with the & rules. Here’s a proof that shows the associativity of &. Your job is to write the justification for each line.

You can re-try auto-check answers without starting over.

When you complete longer proofs like that, which automatically check your answers, here’s a helpful tip: if you get one wrong, you don’t have start the whole problem over. You can put the cursor back in that field, delete your answer, and try again.