Logic and Reasoning Exam

Modus Ponenes

p then q
p
q

Modus Tonens

p then q
~q
~p

Hypothetical Syllogism (1

p then q
q then r
p then r

Hypothetical Syllogism (2

p or q
~p
q

Disjunctive Syllogism

p or q
~q
p

Simplification

p and q
p

Conjuction

p
q
p and q

constructive dilemma

(p then q) and (r then s)
p or r
q or s

addition

p
p or q

De Morgan's Law

~(p and q) = (~p or ~q)
~(p or q) = (~p and q)

Communication

p or q = q or p
p and q = q and p

Assosiation

p or (q or r) = (p or q) or r
p and (q and r) = (p and q) and r

Distribution

p and (q or r) = (p and q) or (p and r)
p or (q and r) = (p or q) and (p or r)

Implication

p then q
~p or q

Transposition

p then q
~q then ~p

Tautology

p = p or p
p = p and p

Exportation

(p and q) then r
p then (q then r)

Equivalence

p == q = (p then q) and (q then p)
p == q = (p and q) or (~q and ~p)

Logical analysis aims at determining whether or not an argument is valid

false

V means in words

or / unless

. Means in words

and / but

== means in words

is equivalent to

Logically Equivalent

the same truth values for literally everything

Consistent

if one row has everything as true

inconsistent

if no row has everyting as true

contradictory

if the values are opposites