Logic and puzzles

Logic is the art of working out what must be true from what you already know. It starts with riddles, liars and Sudoku, and it ends with the tools every mathematician uses to be sure: statements, sets and proofs.

Step	Page	You will be able to
Play	Riddles, clues and Sudoku	Solve puzzles by ruling things out, and spot when a clue makes something impossible
Explore	Knights, knaves and true or false	Solve truth-teller and liar puzzles by trying every case, and use not, and and or carefully
Build	Statements and truth tables	Write statements with symbols, check them with truth tables, and handle if ... then correctly
Master	Sets and "for all, there exists"	Work with sets and Venn diagrams, count with overlaps, and say exactly what "every" and "some" mean
Beyond	How a proof works	Prove things directly, by contrapositive and by contradiction, and break false claims with a counterexample