Choose the symbolic notation translation of the following statements that captures as closely as possible the logical structure of each statement.
if it walks like a duck and talks like a duck, then it's a duck.
( w v t )⊃ d
( w · t ) ⊃ d
( w ⊃ t )⊃ d
~ ( w ⊃ t )⊃ d
if it does not walk like a duck and does not talk like a duck, then it's not a duck.
( w · t ) v ~ d
( ~ w · ~ t ) v ~ d
( ~ w · ~ t ) ⊃~ d
( w ⊃t ) ⊃~ d
if carly works hard and is not distracted, then she will get done on time.
(w v ~ d )⊃ t
(~ w · ~ d )⊃~t
(w ⊃~ d ) ⊃ t
(w · ~ d )⊃ t
use your knowledge of truth tables to identify the following statements as contingent, tautology, or self-contradiction.
p v ~ p
contingent
tautology
self-contradiction
p · ~ p
contingent
tautology
self-contradiction
p v q
contingent
tautology
self-contradiction
if p is true, q is false, r is true, and s is false, determine the truth value of the following:
are these true or false?
[ p v ( q v r ) ] ⊃( s v p )
[ p v ( q · r ) ] ⊃ ~ s
~ ( q · r ) ⊃~ ( s · p )
~ p ⊃ ( ~ s v ~ r )
~ [ p v ( q v r ) ] v ~ ( s v p )
( r · ~ s ) · p