Week 10 - Logic Test Review

Vocabulary flashcards covering symbolic logic concepts from Week 10 notes, including propositional variables, negation, conjunction, disjunction, conditionals, truth tables, and the converse/inverse/contrapositive relationships.

Propositional Variable

A symbol representing a basic statement that can be true or false (examples: p, q, r).

Negation

The operation ~ that inverts the truth value of a proposition (e.g., ~p means 'not p').

Conjunction

The connective ∧ representing 'and'; true only when both components are true (e.g., p ∧ q).

Disjunction

The connective ∨ representing 'or'; true if at least one component is true (e.g., p ∨ q).

Conditional (Implication)

The statement form p → q; reads 'If p, then q'; false only when p is true and q is false.

Truth Table

A table listing all possible truth values for variables and the resulting truth value of a compound statement.

Antecedent

The 'if' part of a conditional statement (p in p → q).

Consequent

The 'then' part of a conditional statement (q in p → q).

Converse

The conditional formed by exchanging the antecedent and consequent of p → q; i.e., q → p.

Inverse

The conditional formed by negating both parts of p → q; i.e., ~p → ~q.

Contrapositive

The conditional formed by negating and exchanging the parts of p → q; i.e., ~q → ~p; logically equivalent to p → q.

Three-Statement Model

Using three propositional variables p, q, r to represent three separate statements in expressions like (p ∧ q) → r.

Symbolic Translation

Converting natural-language statements into propositional symbols using p, q, r and connectives.

p ∧ ~q

A compound that means 'p and not q' (p ∧ ~q).

Truth Behavior of a Conditional

In p → q, the only falsifying assignment is p = true and q = false; other combinations yield true.

p ∨ (q → r)

A disjunction where the second disjunct is an implication; used to illustrate complex truth tables.

Contrapositive Equivalence

The contrapositive (~q → ~p) is logically equivalent to the original p → q.