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1. Translate the below statement fully into propositional form. Barry and Mary went for a swim. 2. Translate the below statement fully into propositional form.The frogs are dancin
1. Translate the below statement fully into propositional form.
Barry and Mary went for a swim.
2. Translate the below statement fully into propositional form.
The frogs are dancing under the bridge provided that either the moon is out or the bats aren't about.
3. Fully translate the below argument into propositional form.(Here's that funny symbol: Ⱶ)
The piano is out of tune. If Bob is playing when it is Saturday, then the piano isn't out tune. So, Bob isn't playing.
4. Determine by the brief truth table method whether the below argument is valid.
(J&S)→C ⊢ ~C→~(J→S)
5. Determine by the brief truth table method whether the below argument is valid.
P→B, (C → ~L) → (P & ~B) ⊢ L & C
6. 1. Provide a propositional translation for the below. 2. Determine whether it is valid by the brief truth table method.
If the garage door is open when everyone is away, the raccoons will get in. Either the garage door is open or everyone is not away. So, the raccoons will get in.
7. Determine whether the below is valid by the tableaux method.
(E v D) & L, D→L ⊢ E
8. Determine whether the below is valid by the tableaux method.
(G & ~L) → (R v S), ~(G→L) ⊢ ~S→R
9. 1. Provide a propositional translation for the below. 2. Determine whether it is valid by the tableaux method.
If the goats are hungry when the sheep are, Bob and Mary have to get to work. Neither Bob nor Mary have to get to work. Therefore, the goats aren't hungry.
10. Fully translate the below sentence into predicate form. (Relational predication is not needed.) (Here's those funny symbols: ∃ ∀)
"Neither John nor Bob are fishing."
11. Fully translate the below sentence into predicate form. (Relational predication is not needed.) (Here's those funny symbols: ∃ ∀)
"Some bar is open."
12. Fully translate the below argument intopredicate form. (No relational predication is needed.) (Here's those funny symbols: ∃ ∀ Ⱶ)
Some of the cakes taste foul if Bob is working. None of the cakes taste foul. So, someone isn't working."
13. Fully translate the below sentence into relational predicate form. (Here's those funny symbols: ∃ ∀)
"Mary's cat is sick."
14. Fully translate the below sentence into relational predicate form. (Here's those funny symbols: ∃ ∀)
"Some primates eat monkeys."
15. Fully translate the below argument into relational predicate form. (Here's those funny symbols: ∃ ∀ Ⱶ)
Everyone likes someone. Bob likes no one if he has nothing. So, Bob has something.
16. Test the below for validity by tableaux.
∀x(Cx → ~Wx), ∃y(Wy & Sy) ├ ~∃z(Sz & ~Cz)
17. Test the below for validity by tableaux.
∀x∀y(Ey → Jx), ∀x(∀yEy v Lx) ├ ∀x(Jx v Lx)
18. Translate the below argument intopredicate form and test for validity by tableaux. (No relational predication is needed.)
"Larry, the goat, is in the field if someone left the gate open. Bob left the gate open. Hence, some goat is in the field."
19. Translate the below argument into relational predicate form and test for validity by tableaux.
"Tigers eat humans. Bengals are tigers. Hence, bengals eat humans."
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