Section Progress:

10.2 &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:

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 to want. For example, like this:

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.

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.

10.2 &Intro