This section includes a traditional range of topics from logic as they are taught in a Discrete Mathematics course. The material is roughly equivalent to 8 hours of lectures, and should take a first-year student about 4 weeks to assimilate.

The known difficulties in learning logic are mostly to do with the development of symbolic thinking and the intuition and techniques of symbol manipulation. Learners often find it a problem to pitch their reasoning at the right level of formality, with the stronger students tending to overformalise their argument whereas the weaker ones seek a "magic spell" to make it sound formal. One of the simpler (but infinitely more annoying) problems is the converse and inverse errors in dealing with implications. Generations of students have failed their assessment by not showing enough understanding there, so in the present edition of "Logic", I have included the whole slide on this issue.

As in every other discipline, practice makes perfect in logic.
To this end a range of exercises has been designed,
located here.
Here are some solutions. And now a **
thesaurus is available! **

Enjoy!

The Author

**Logic: table of contents**

- The concept of logic
- Propositions
- Logical connectives
- Logical connectives (1)
- Logical connectives (2)
- Implication
- Some equivalencies
- Instantiation and substitution
- Valid argument
- Valid argument (example)
- Rules of inference
- Modus Ponens
- Modus Tollens
- Hypothetical Syllogism
- Other inference rules
- Validating the argument
- The idea of calculus
- Predicates
- Predicates (2)
- Negating Quantifiers
- Instantiation of predicates
- Theorems and proofs
- Axiomatic theory (example)
- Axiomatic theory (example) (2)
- Axiomatic theory (example) (3)
- Axiomatic theory (example) (4)
- Proof techniques
- Existence proofs
- Principle of mathematical induction
- Why is PMI valid?
- Program verification
- Inference rules for programs
- Program verification (example)

© 1991-1997 by A.Shafarenko

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Copying any material referenced directly or indirectly on this page is permitted only as part of a degree course at Surrey University, England and only for the duration of the course. Any form of distribution of the audio, graphic or typeset data constituting the files linked up, directly or indirectly, to this page is prohibited without the prior written permission of Dr Alex Shafarenko.