definitions
the sentence cannot be false
What is logical truth?
Is this a sentence of SL? why or why not?
∨ Q
No! the disjunction needs two components in order to be a sentence of sl
label the main connective of the following sentence:
~ (A ⊃ B)
Negation!
Ted has red all of the books A Fine Red Rain, Bury Your Dead, The Old Fox Deceived, and Rough Country
KEY:
F: Ted has read A Fine Red Rain
B: Ted has read Bury your Dead
D: Ted has read The Old Fox Decieved
R: Ted has read Rough Country
(F & B) & (D & R)
T | F
F | T
What is the truth table for ~P?
it's not possible for all of the premises to be true and the conclusion false
What is logical validity?
is this a sentence of SL? why or why not?
K & L
yes, the outermost parentheses can be dropped
label the main connective of the following sentence:
~ (A = B) & (~ C ⊃ D)
Conjunction!
Ted has read at least one of the books A Fine Red Rain, Bury Your Dead, The Old Fox Deceived, and Rough Country
KEY:
F: Ted has read A Fine Red Rain
B: Ted has read Bury your Dead
D: Ted has read The Old Fox Decieved
R: Ted has read Rough Country
(F v B) v (D v R)
P is true in every instance except for when the Premise is true and the conclusion is false.
What is the truth table for a material conditional?
when you have two sentences and it is not possible for one sentence to be true while the other is false
what are logically equivalent sentences?
name the one unary connective of SL, and the binary connectives
binary: conjunction, or apersand
material conditonal or horseshoe
material biconditional or triple bar
disjunction or wedge
label the main connective and identify the immediate components of the sentence:
~ (S & G) ∨ B
main connective: disjunction
immediate components:
~ (S & G), (S & G), B
Ted hasn't read any of the books A Fine Red Rain, Bury Your Dead, The Old Fox Deceived, or Rough Country
KEY:
F: Ted has read A Fine Red Rain
B: Ted has read Bury your Dead
D: Ted has read The Old Fox Decieved
R: Ted has read Rough Country
(~ F & ~ B) & (~D & ~ R)
The conclusion is true if and only if both premises are true or both premises are false.
What is a material bi conditional?
when an argument is logically valid and all of its premises are true
What is a logically sound argument?
what are the immediate components of a conjunction called? of a disjunction? of a material conditional?
conjunction: conjuncts
disjunction: disjuncts
material conditional: antecedents and consequents
label the main connective, the immediate components, and all sentential components of the sentence:
~ (A = B) & (~ C ⊃ D)
main connective: conjunction
immediate components: (A=B), (~C⊃ D)
All components:
~ (A = B) & (~ C ⊃ D)
(A = B) & (~ C ⊃ D)
(A=B), ~ (A = B)
(~ C ⊃ D)
A, B, D, ~C, C
Ted has read one but not both of the books A Fine Red Rain and Bury Your Dead
KEY:
F: Ted has read A Fine Red Rain
B: Ted has read Bury your Dead
D: Ted has read The Old Fox Decieved
R: Ted has read Rough Country
( F v B ) & ( B & ~ F )
The first sentence is false and the second sentence is true, the conclusion is true.
What is a disjunction?
When it is impossible for the members of a set to be true and that sentence false.
What is logical entailment?
is this a sentence of SL? why or why not?
(F =K) ⊃ [M ∨ K]
yes! you can interchange brackets and parentheses
label the main connective, the immediate components, and all the sentential components of the sentence:
[A & ~ (B ∨ C)] ⊃ [(A & ~ B) & (A & ~ C)]
main connective: conditional
immediate components:
A & ~ (B ∨ C), (A & ~ B) & (A & ~ C)
all sentential components:
[A & ~ (B ∨ C)] ⊃ [(A & ~ B) & (A & ~ C)]
A & ~ (B ∨ C)
~ (B ∨ C), (B v C)
(A & ~ B) & (A & ~ C)
(A & ~ B), (A & ~ C)
A, B, ~ B, C, ~ C
Ted has read exactly two of the books A Fine Red Rain, Bury your Dead, and The Old Fox Deceived
KEY:
F: Ted has read A Fine Red Rain
B: Ted has read Bury your Dead
D: Ted has read The Old Fox Decieved
R: Ted has read Rough Country
[(F & B) & ~ D] v ([(F&D) & ~B] V [(B & D) & ~ F])
T T| T
T F| F
F T | F
F F | F
What is a conjunction?