Logic and Mathematical Proof

What the page covers

The resources run from first steps in logic to full proof methods. The note on conditional statements and converses explains how "if, then" statements are built, and the flashcards on definitions in chapter 2 cover conjecture, counterexample, converse, inverse, contrapositive and the biconditional. Further along are decks on rules of inference, predicate logic, quantifiers and proof by induction.

Where to start

Begin with the basics of conditionals. Read the note on conditional statements and converses, then run through the deck of definitions. Next, open the flashcards on logical equivalences and the deck on truth tables and logic laws, which show how two expressions can be shown to match.

1. Conditionals, converses and definitions.
2. Truth tables and equivalences.
3. Rules of inference and predicates.
4. Direct proofs and mathematical induction.

Using maps and quizzes together

There are many mind maps on proof strategy, proving conditional statements and logical reasoning. Several have matching notes created from them, so you can read a map as text if you prefer. The mind map called Six Concepts of Discrete Mathematics MAT1348 links truth tables with simplifying expressions and testing whether statements hold.

Use a map to see the shape of a method, then test yourself. The quizzes on logic, pure logic and reverse syllogisms check your reasoning. The quiz on triangle congruency proofs gives geometry practice. Some quizzes are aimed at reasoning tests, so choose those that suit your goal.

Geometry and set links

Some resources apply proof to geometry, such as the flashcards on properties, definitions, theorems and postulates, and the notes on theorems 2.1 to 2.5. Others link logic to sets, including the mind map on sets, Venn diagrams and propositions. The slide sets on series and matrices show induction at work. A few resources are tagged for A-level Maths.

Where it fits

This unit sits in the strand Logic, Sets and Discrete Mathematics, within Mathematics. Most resources suit university study, with a good share for school students. Pick a resource that matches your stage, take a quiz, and then make your own flashcards or maps from what you found hard.