Core Concepts
Does this sentence have a truth value:
Cats are the best pets.
Sentences with opinions still have truth values.
What is logical validity?
Impossible for the premise to be true and the conclusion false!!!
Is this a correct sentence of SL?
& H
no!
The negation is the only symbol that can have only one letter
Betty and Ollie are tuxedo cats.
(B & C)
Symbolize and paraphrase the following sentence:
Ollie and Betty will both get a toy, or neither of them will.
(O&B) wedge negation (O&B)
Ollie and Betty will both get a toy, or it is not the case that Ollie and Betty will get a toy.
Does this sentence have a truth value:
Come here cat.
No!
Commands do not have truth values
What is logical soundness?
Logically valid AND all premises are true
Is this a correct sentence of SL?
M ~ N
no!
a negation can only apply to one letter, this sentence needs another sentence to connect the two
Symbolize the following sentence:
Ollie is not an orange cat.
Negation O
Symbolize and Paraphrase the following sentence:
If Ollie has to go to the vet, then so will Betty, and if Gizmo has to go to the vet then so will Betty.
(O horseshoe B) & (G horseshoe B)
There are more cats in Columbia than dogs.
Yes!
Even if we aren't sure of the truth-value, it still is an argument.
What is the difference between logical equivalence and logical entailment?
(All truth values are identical)
Entailment: Impossible for all parts of set to be true and the sentence false
Is this a correct sentence of SL?
J ⊃ (K ⊃ (A ∨ N))
yes!
You can omit the first parentheses if there are two outermost parentheses
Symbolize the following sentence:
Either Ollie or Patches are kittens.
(O wedge P)
Symbolize and Paraphrase the following sentence:
Either Ollie won't get a treat or Betty and Ollie will get one.
Negation O wedge (B&O)
Does this sentence have a truth value:
Is your cat orange?
No!
Questions do not have truth values.
Is this true or false?
The premises of a logically valid argument always provide support for the conclusion of the argument.
False :)
not every logical valid argument is sound as well
what kind of sentence is this?
~ ~ (A ⊃ B)
negation
Symbolize the following sentence:
If Ollie wants to play then so will Betty.
O horseshoe B
Ollie and Betty will get a treat if and only if Ollie and Betty go to the vet.
(O&B) triple bar (P&M)
Does this sentence have a truth value:
Do you really need another cat?
Trick question.
The answer is both yes and no depending on the context of the speaker.
Is this true or false?
Any argument that includes among its premises ‘Everyone is a scoundrel’ and ‘I’m no scoundrel’ is logically valid.
yes
what kind of sentence is this?
[A & ~ (B ∨ C)] ⊃ [(A & ~ B) & (A & ~ C)]
Conjunction!
Symbolize the following sentence:
Ollie will go play if Betty is playing
(B horseshoe O)
Ollie won't get a treat if Betty will, but Ollie will get a treat if Gizmo does
(B horseshoe negation O) & (G horsehoe O)