Math 10 - Module 5

propositions

declarative sentence that can be assigned a truth value of either true or false

lowercase letters

used to represent propositions

questions, exclamations, and imperatives

not considered as propositions

conjunction “p and q”

p ∧ q

disjunction "p or q"

p ∨ q

conditional "If p then q"

p → q

conditional: proposition p is called

antecedent

conditional: proposition q is called

consequent

biconditional "p if and only if q"

p ↔ q

negation "not p”

~p

AND (∧) rule

TRUE ∧ TRUE = TRUE
Anything else = FALSE

OR (∨) rule

TRUE ∨ TRUE = TRUE
TRUE ∨ FALSE = TRUE
FALSE ∨ FALSE = FALSE

NOT (~)

~TRUE = FALSE
~FALSE = TRUE

IF...THEN (→)

all except TRUE → FALSE = FALSE

↔ (same as / equivalent)

TRUE ↔ TRUE = TRUE
FALSE ↔ FALSE = TRUE
TRUE ↔ FALSE = FALSE

compound proposition

proposition formed by combining simpler propositions using logical connectives

implication

relationship where proposition p materially implies proposition q

equivalence

relationship where two propositions have the same meaning or can be substituted for one another

~q → ~p

contrapositive of p → q

q → p

converse of p → q

~p → ~q

inverse of p → q

Euler diagram

represents propositions, the way Venn diagrams represent sets

fallacy

p is false and q is true; p is false and q is true

Ad Populum

argument is assumed to be valid since many people believe in it

Appeal to Authority

argument is claimed to be valid because a famous or famous person, who is not an expert in the pertinent field, supports

False Cause

fallacious argument correlates two events, even if unrelated

deductive reasoning

process of reasoning from a general proposition to a specific instance

inductive reasoning

process of reasoning from specific instances to a general proposition