Level 4: Statements and truth tables

Logic and puzzles · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 you used not, and, or and if in words. In this level they get symbols, and you meet the tool that checks any argument made of them: the truth table, which tries every possible case at once. You find out why "if ... then" is true whenever its first part is false, which turned-around versions of a sentence mean the same thing, how a computer program makes choices, and how to win a game every time by working backwards from the end.

Lesson	You will be able to
Statements and letters	Tell statements from other sentences, and write sentences with \(\neg\), \(\land\) and \(\lor\)
Truth tables	Build a full truth table for two or three letters, and use it to show two statements say the same thing
The conditional	Explain the table of \(p \to q\), including why a false "if" part makes it true, and use "if and only if"
Converse, inverse and contrapositive	Write all three for any if-then statement and say which one always means the same as the original
Coding with conditions	Write and trace programs with if, else and nested conditions, such as sorting odd and even or classifying triangles
Winning strategies	Win one-pile Nim every time by leaving a multiple of 4, and find winning moves by working backwards

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