Master Propositional Logic: 45 Flashcards on Connectives, Truth Tables and Proof Methods

Propositional logic is the part of logic you can compute: the truth value of a compound statement depends on nothing but the truth values of its parts, so any question about validity can in principle be settled by a table. The Flip It deck Propositional Logic & Truth Tables (FG8898) covers that system in 45 accurate, well-scoped cards, from the five connectives up to sequent calculus. One warning: it never shows an actual truth table. You have to draw those yourself — which turns out to be the best way to use it.

What the cards look like

Also covered: bivalence, the law of excluded middle, contingency, atomic and molecular formulas, propositional variables, truth-functionality, validity versus soundness, hypothetical and disjunctive syllogism, XOR, NOR, functional completeness, analytic tableaux and branch closure, Hilbert systems, natural deduction, Gentzen sequent calculus, double negation, p → q ≡ ¬p ∨ q, and the quantifier boundary with first-order logic.

Build the tables the deck leaves out

Before your second session, write the four-row table for each of the five connectives on a single sheet. Two of them cause nearly all the errors: implication is true whenever the antecedent is false (F → anything is T), and disjunction is inclusive — p ∨ q is still true when both are true. XOR is the one that is not. Once that sheet exists, the cards on tautology, contradiction and contingency become mechanical instead of verbal.

Annotate the bivalence card

Cards 3 and 23 read like duplicates: bivalence says every proposition has exactly one of two truth values, excluded middle says every proposition is either true or false. They are not the same claim. Bivalence is semantic, about the values a model may assign; excluded middle is a formula of the system, p ∨ ¬p. The distinction becomes concrete in intuitionistic logic, where p ∨ ¬p is not a theorem. Add that line to card 23 rather than deleting either card.

One correction worth making

Card 33 says a tableau closes when every branch contains a contradiction, proving the original formula was contradictory. True, but it hides the technique you will actually be graded on: to prove that φ is a tautology, you run the tableau on ¬φ and show that it closes. Rewrite the back to include that step, or the proof-method cards stay abstract.

Order of attack

Cards 0–31 are semantics: connectives, truth values, argument forms. Cards 32–36 jump into proof systems (tableaux, Hilbert, natural deduction, sequent calculus) at a visibly higher level — treat them as a preview, not as memorisation. Cards 37–44 are the equivalence laws, the cheapest points on any exam: De Morgan, double negation, implication as ¬p ∨ q.

For the surrounding discrete-maths material (graphs, sets, combinatorics), pair this with the Discrete Mathematics study guide.

The deck is FG8898 — Propositional Logic & Truth Tables; find it in your library at flip-it.app.