**Q:** What is a truth tree?

**A:** A truth tree is a diagram that shows a set of compound propositions decomposed into literals following standard decomposition rules.

**Q:** What is a literal?

**A:** A simple proposition symbolized as a constant or variable, or the negation of the same.

**Q:** What does it mean to decompose a compound proposition?

**A:** It means to show the components that must be true for the decomposed proposition to be true. A fully decomposed proposition is broken down into literals.

**Q: **Why do some compound propositions branch when decomposed?**
A: **The branching shows that there is more than one way for the proposition to be true.

**Q:** What does consistency mean?

**A:** Consistent propositions can all be true at the same time.

**Q:** How does the truth tree show consistency?

**A:** If the propositions in the set are fully decomposed into literals on at least one branch without contradiction, the propositions are consistent.

**Q:** What does it mean to recover the truth values?

**A:** It means to show the truth values of the component propositions that make every proposition in the given set true.

**Q:** What does SM mean?

**A:** It stands for Set Member; a label for a proposition in the given set.

**Q:** What is the meaning of the number and the symbols at the end of a row?

**A:** It is the justification for the decomposition, showing the number of the compound proposition that is decomposed, and the abbreviation of the rule used to decompose it.

**Q:** What is the meaning of the Ο at the bottom of a truth tree branch?

**A:** It designates an open branch, meaning that there are no contradictions on that branch.

**Q:** What is the meaning of the numbers separated by an Χ at the bottom of a branch?

**A:** The X designates a closed branch; the numbers are the line numbers of the propositions that contradict on that branch.

**Q:** What is the benefit of using truth trees?

**A:** Truth trees do the same things as truth tables — showing consistency, equivalence, validity, etc. — but in a visual way. They are a tool used in higher-level logic.