Finite Test Study Notes
Unit 6 – Logic
Statements
· Statement – Declarative sentence that is either true or false
· Logical Connectives – Combining statements with and, or, if… then…, not
· Compound Statement – Multiple statements combined with connectives
· Negation – Makes a true statement false, or vice versa
· Symbolic representation of statements – use ∧, ∨, ~, →
· Truth tables – Show all possible inputs, and determine all truth outputs
· AND – Both statements are true (Conjunction)
· OR – Either statement is true (Disjunction)
Truth Tables and Equivalent Statements
· Complete truth tables for compound statements
· Two statements with the same final truth values are equivalent
· De Morgan’s Laws ∼(p∨q)≡∼p∧∼q ∼(p∧q)≡∼p∨∼q
The Conditional
· Know the if… then… truth table, False only when true→false
· Combine compound statements with conditionals
· Equivalent statements listed on page 245 of text
· Other words can be used to signify if… then…
· Converse – Switch hypothesis and conclusion
· Inverse – Negate both the hypothesis and conclusion (same as converse)
· Contrapositive – Negate and switch hypothesis and conclusion (same as original)
· Biconditional – “if and only if” ↔ only true with both statements have same value
Arguments and Proofs
· Tautology – Truth table true for all possible inputs
· Modus Ponens
· Modus Tollens
· Disjunctive Syllogism
· Transitivity
· Fallacy of Converse
· Fallacy of Inverse
Analyzing Arguments with Quantifiers
· Quantifiers change the quantity involved in the logical argument
· Universal Quantifiers – all, each, every, no(ne) ∀x[cx→sx]
· Existential Quantifiers – some, there exists, (for) at least one ∃x[cx∧fx]
· Venn Diagrams can help to analyze quantifiers
· Negation of quantifiers changes universal into existential
· Be prepared to negate and put into words