1. Formal Logic
CSC 333

2. How about some examples?
Look at Exercises 1.1.

3. Propositional Logic
A valid argument is composed of hypotheses (given statements) and a conclusion.
Note examples 9 and 10.
If the conclusion inevitably follows from the hypotheses, this form of argument is called modus ponens.

4. Proof Sequence
To prove that a conclusion Q is valid based on a set of hypotheses, we start with the hypotheses,
Then we apply a derivation rule (what’s that?).
A way to “manipulate wffs in a truth-preserving manner” by substituting an equivalency for a hypothesis.
Example: Q v P  P v Q

5. Inference Rules See Table 1.13 Note modus ponens.
These rules are almost self-evident.
Try Practice 10, p A next step, anyone?
Read Example 14 as a good example of derivation rules.

6. Some Heuristics Trial and error. Blind alleys happen!
There often is more than one way to arrive at a correct proof sequence
Try to use modus ponens often.
Convert wffs of the form (P ^ Q)’ , (P v Q)’, P v Q to more useful forms (hints, p. 27).
Experience helps!

7. More good stuff . . . The deduction method Hypothetical syllogism
Additional rules proved by using rules known to be true.
See Table 1.14.

8. Mentioned last time . . . Notable terms: Modus ponens Modus tollens
Valid argument
Equivalence rules
De Morgan’s laws
Hypothetical syllogism
Quantifiers

9. Quantifier?
For all . . .
There exists . . .