Level 5: Sets and arguments

Logic and puzzles · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you wrote statements with letters and checked them with truth tables. In this level the same ideas grow in two directions. First, sets: collections of things, pictured with Venn diagrams, where or, and and not become union, intersection and complement. Second, arguments: how "for all" and "there exists" work, which steps of reasoning are always safe, and which tempting steps are traps.

Lesson	You will be able to
Sets	List and describe sets, use \(\in\) and \(\subseteq\) correctly, explain the empty set, count subsets, and place numbers in \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\), \(\mathbb{R}\)
Union, intersection, complement	Combine sets, shade regions of two- and three-set Venn diagrams, and see each region as a row of a truth table
De Morgan's laws	Prove De Morgan's laws three ways, and write the opposite of and, or, inequalities and if sentences correctly
Quantifiers	Read and write \(\forall\) and \(\exists\), decide when they are true, negate them, and explain why their order matters
Valid arguments	Recognise modus ponens, modus tollens, chains and syllogisms, check validity with truth tables, and solve Lewis Carroll's puzzles
Fallacies	Spot affirming the consequent and denying the antecedent, disprove a bad argument with a counterexample, and tell valid from sound

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