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Solutions of Reinforcement Learning 2nd Edition (Original Book by Richard S. Sutton,Andrew G. Barto) How to contribute and current situation (9/11/2021~) I have been working as a full-time AI engineer and barely have free time to manage this project any more.
- J. Robert Loftis Robert Trueman
- Fall 2021
- Arguments
- Valid arguments
- Socrates is a carrot.
- Bob is now 20 years old.
- Other logical notions
- Connectives
- (M ∨ (C ∨ G))
- ((A ∨ B) ∧ ¬(A ∧ B))
- (S ∨ C ) ,
- (¬A ↔ B) (¬(¬A∧ ¬B) ∧ ¬(A∧ B))
- (H → I ) ∨ (I → H ) ∧ ( J ∨ K)
- ∨ (H → ) ∨ I → )
- ∨ ( J ∨ K)
- Complete truth tables
- (A↔B)↔¬ (A↔¬B)
- ∧B)→(B ∨A)
- ∧ B) ∧ ¬(A ∧ B) ∧ C
- 8. B) ∧ C ] → B
- 5. ‘ ’ and ‘ ’ have the same truth table
- 4. (D ∨ E)] ∧ ¬C
- ¬(G ∧ (B ∧ H )) ↔ (G ∨ (B ∨ H ))
- 5. O) ↔ A] → (¬D ∧ O)
- 5. (B ∧ ¬B)] [(A ∧ B) ↔ B] → (A → B)
- → A A ↔
- T T T
- 5. , (A → B) → C A → , C
- ¬B A →
- → B B ∴
- A B
- A,B ⊨ C
- A B C
- A B
- A B not
- A B
- A B
- Truth table shortcuts
- ∧ ¬B B
- D ¬D ∨D
- ¬ (A ∧B)↔A
- D (B ∧D)↔ [A↔(A ∨C )]
- Partial truth tables
- 8. B) → , (¬B ¬A)
- B) ↔ (¬A ∧ ¬B)
- ¬ ((C ∨ A)
- ((A ∧ B)
- 10. C ) ∨ (B ∧ D)]
- 10. , B → ¬A ¬B ,
- Proof-theoretic concepts
- ⊢ B (A∧ C) ⊢
- ? Explain your answers.
- Hint
- A ↔ B
- A B
- B A
- Practice exercises
- Sentences with one quantifier
- Barbara.
- B(x) : O (x) : ∀x(D(x)
- D(x) : x is a dog S (x) :
- Identity
- x y
- Definite descriptions
- W (x) :
- T (n) ∧ ∀y(T (y) → n
- Consider the following interpretation:
- Using Inter-pretations
- J (a) K (a)
- Something is H. No G are F. All H are G. So: Some H is not F
- G (a)
- And ofer a proof of it.
- Normal forms
remixed and revised by Aaron Thomas-Bolduc Richard Zach
This booklet is based on the solutions booklet : , by Tim Button
Highlight the phrase which expresses the conclusion of each of these arguments: It is sunny. So I should take my sunglasses. It must have been sunny. I did wear my sunglasses, after all. No one but you has had their hands in the cookie-jar. And the scene of the crime is littered with cookie-crumbs. You’re the cul-prit! Miss Scarlett and Professor P...
Which of the following arguments is valid? Which is invalid? Socrates is a man. All men are carrots. ∴
Valid Abe Lincoln was either born in Illinois or he was once president. Abe Lincoln was never president. ∴ Abe Lincoln was born in Illinois. Valid If I pull the trigger, Abe Lincoln will die. I do not pull the trigger. ∴
Valid An argument is valid if and only if it is impossible for all the premises to be true and the conclusion false. It is impossible for all the premises to be true; so it is certainly impossible that the premises are all true and the conclusion is false. Could there be: A valid argument that has one false premise and one true premise? Yes. Exampl...
For each of the following: Is it necessarily true, necessarily false, or contingent? Caesar crossed the Rubicon. Contingent Someone once crossed the Rubicon. Contingent No one has ever crossed the Rubicon. Contingent If Caesar crossed the Rubicon, then someone has. Necessarily true Even though Caesar crossed the Rubicon, no one has ever crossed the...
Using the symbolization key given, symbolize each English sentence in TFL. M : Those creatures are men in suits. C : Those creatures are chimpanzees. G : Those creatures are gorillas. Those creatures are not men in suits. ¬M Those creatures are men in suits, or they are not. (M ∨ ¬M ) Those creatures are either gorillas or chimpanzees. (G ∨ C ) Tho...
Using the symbolization key given, symbolize each English sentence in TFL. : Mister Ace was murdered. : The butler did it. : The cook did it. : The Duchess is lying. E : Mister Edge was murdered. F : The murder weapon was a frying pan. Either Mister Ace or Mister Edge was murdered. ∨ E) If Mister Ace was murdered, then the cook did it. → C ) 3. If ...
Give a symbolization key and symbolize the following English sen-tences in TFL. F : There is food to be found in the pridelands. R : Rafiki will talk about squashed bananas. A : Simba is alive. K : Scar will remain as king. If there is food to be found in the pridelands, then Rafiki will talk about squashed bananas. (F → R) Rafiki will talk about s...
3. If Zoog remembered to do his chores, then things are clean but not neat. If he forgot, then things are neat but not clean. There-fore, things are either neat or clean; but not both. Z : Zoog remembered to do his chores C : Things are clean N : Things are neat (Z → (C ∧ ¬N )) (¬Z → (N ∧ ¬C )) ∨ , , ((N C ) ∧ ¬(N ∧ C )) . For each argument, write ...
But if we wanted to symbolize it using only one connective, we would have to introduce a new primitive connective.
The scope of the left-most instance of ‘ ’ is ‘ → (I → The scope of the right-most instance of ‘ ’ is ‘ ’. H ) ’.
The scope of the left-most instance of ‘ is ‘ (I H ’
The scope of the right-most instance of ‘ ’ is ‘ ’ The scope of the conjunction is the entire sentence; so conjunction is the main logical connective of the sentence.
Complete truth tables for each of the following: → A → ¬C A→A T T T T T F F F
T T T T F F T F F F T T T F F T F F T F T T F T F F T F B (A→B) ∨ (B →A) T F T F T T T T T F F F T T T T T T F F T T F F T F
T F T F T T T T T T F F T T T T F T T T F T F F F F F
B (A ∧B)∧¬ (A ∧B) ∧C T T F F T T F F F T T T F F T T T T F T T T F F T T T F T F F FT T F F F T T F F FT T F F F F F F F T FT F F T T F F F T FT F F T F F F F F FT F F F T F F F F F FT F F F F [(A ∧
B [(A ∧B) ∧C ] →B T T F F T T F F T T T T T T T T T T T F F T T T F F F T F T T F F F F F T F F T F T T T F F T F F T T F F F F T F T F F F F F F F
Indeed they do: Write complete truth tables for the following sentences and mark the column that represents the possible truth values for the whole sentence.
[C ↔ ∨ (D E)] ∧ ¬ C T T F F T T T F T T T F F T F F F T F T F F F T F F F T F F T F T F
5. ¬ (G T T T T F F F F ∧ (B ∧ H)) ↔ (G ∨ (B T T T T T F T T F T T F F F T F T T F T T F F T F T F F F F F F ∨ H)) T F T F F T F T F F Write complete truth tables for the following sentences and mark the column that represents the possible truth values for the whole sentence.
¬ [(D ↔ O) ↔ A] → ¬ ( D ∧ O) T T T F F T T T F F F T T F T F F F T F F F F F F T T T T T F T F T T T F F T T F F F F F T F F If you want additional practice, you can construct truth tables for any of the sentences and arguments in the exercises for the previous chapter.
6. Contingent Contradiction Contradiction Contingent Determine whether each the following sentences are logically equiva-lent using complete truth tables. If the two sentences really are logically equivalent, write “equivalent.” Otherwise write, “Not equivalent.” ¬A and A ∧ [(A ¬A ¬B ↔ B and ∨ B) ∨ C ] and [A ∨ (B ∨ C )] ∨ (B ∧ C ) (A ∨ B) ∧ (A ∨ C...
and A ¬(A → B) ¬A → ¬B and ∨ B ¬A → and B → B) → C A → (B → C ) and A ↔ (B ↔ C ) A ∧ (B ∧ ) C and Determine whether each collection of sentences is jointly satisfiable or jointly unsatisfiable using a complete truth table. ∧ → → ¬B ¬(A , B) B A , ∧ ¬ ¬ → B) F T T T F T T F F T F T F F F F ∨ B A , ¬A B → ¬B , → Consistent
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
Consider the following sentences: ¬(A ↔ B) ¬B) (¬A ∨ ¬(A ∧ B)) (¬(A → B) ∧ (A → C )) (¬(A ∨ B) ↔ ((¬C ∧ ¬A) → ¬B)) ((¬(A ∧ ¬B) → C ) ∧ ¬(A ∧ D)) For each sentence, find a tautologically equivalent sentence in DNF and one in CNF.
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midterm 1 answer key math 249 math 265 midterm fall 2021 exam version: 11 part multiple choice instructions: choose the best answer to each of the following
Aaron Thomas-Bolduc & Richard Zach University of Calgary. It includes additional material from forallx by P. Magnus, used under a CC BY 4 license, and from forallx: Lorain County Remix, by Cathal Woods and J. Robert Loftis, and from A Modal Logic Primer by Robert Trueman, used with permission.
University of Calgary It includes additional material from forall x by P.D. Magnus, used under aCC BY 4.0license, and from forall x: Lorain County Remix, byCathal Woodsand J. Robert Loftis, used with permission. This work is licensed under aCreative Commons Attribution 4.0li-cense. You are free to copy and redistribute the material in any medium
MindTap: View Answer Keys. View Answer Keys. View the correct answers for activities in the learning path. This procedure is for activities that are not provided by an app in the toolbar. Some MindTap courses contain only activities provided by apps. Click an activity in the learning path. Turn on Show Correct Answers. View Aplia Answer Keys ...
Click the links below to view the Student Answer Keys in Microsoft Word format. Answer Key - Chapter 01 (23.0K) Answer Key - Chapter 02 (20.0K) Answer Key - Chapter 03 (44.0K) Answer Key - Chapter 04 (32.0K) Answer Key - Chapter 05 (34.0K) Answer Key - Chapter 06 (30.0K) Answer Key - Chapter 07 (39.0K) Answer Key - Chapter 08 (40.0K) Answer Key ...
