# Must we do every unit of Intermediate Logic?

A common question for new parents, teachers, or tutors going into Intermediate Logic:

“Intermediate Logic is a challenging course, especially trying to complete it all in one semester. Is each unit equally important, or can I skip something if I can’t fit it all in?”

The short answer is “You don’t have to do it all.” Unit 1 on Truth Tables is foundational to propositional logic, as is Unit 2 on Formal Proofs. Both of these are essential and must be completed by every student. Unit 3 teaches the Truth Tree method. A truth tree is another tool that does the same job as a truth table: determining consistency, equivalence, validity, etc. Some people like truth trees more than truth tables, since they are more visual. But Unit 3 could be considered an optional unit. Unit 4 covers Applying the Tools to Arguments. This is where the rubber meets the road for propositional logic, showing how to apply what has been learned up to this point to real-life reasoning. Consequently, Unit 4 should be completed by every student. Note that if you skip Unit 3, one question in Unit 4 will have to be skipped (namely, Exercise 28c #1). Unit 5 on Digital Logic – the logic of electronic devices – is entirely optional. Like Unit 4, this unit covers a real-life application of the tools of propositional logic, but one that is more scientific (though ubiquitous in this age of computers and smart phones). Though optional, many students find that they really enjoy digital logic.

It is common for teachers to skip either truth trees or digital logic. In fact, only the best classes successfully complete both Unit 3 and Unit 5. The Teacher Edition of the Intermediate Logic text includes two different schedules, one for completing every unit, and another for skipping Unit 5.

# Rules for Guessing

Shorter truth tables can help us find if an argument is valid, or a set of propositions are consistent, or if two propositions are equivalent. However, when completing a shorter truth table, we must sometimes guess a truth value for a variable. This occurs when there are no “forced” truth values — that is, when there exists more than one way to complete the current truth value for every remaining proposition.

Here are two rules to keep in mind when you must guess a truth value:

1. If guessing allows you to complete the shorter truth table without contradiction, then stop; your question is answered. Either you have shown the argument is invalid, or the given propositions are consistent, or the two propositions are not equivalent.
2. If the guess leads to an unavoidable contradiction, then you must guess the opposite truth value for that variable and continue, because the contradiction just might be showing that your guess was wrong.

Take a look at this post for a flowchart for guessing with validity.