I’m in a bind. I need help with the questions below. The help would be greatly appreciated. *Note:  that on the truth-table questions, vertical alignment and underlining (or otherwise...

I’m in a bind. I need help with the questions below. The help would be greatly appreciated.

*Note:  that on the truth-table questions, vertical alignment and underlining (or otherwise highlighting) are important parts of the answer. Take care when formatting these.   

1: Symbolize the following sentence, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Communication will be lost if and only if Hal goes crazy.

2: Symbolize the following sentence, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

It’s not the case that both communication will be lost and Dave will fly into the monolith.

3: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Dave will not fly into the monolith unless Hal goes crazy.

4: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Only if Hal goes crazy and everyone aboard is killed will Dave fly into the monolith.

5: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Communication will be lost if Frank doesn’t replace the AE-35 until, and Dave will fly into the monolith only if everyone on board is killed.

6: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Dave will not fly into the monolith if and only if Hal doesn’t go crazy, provided Frank replaces the AE- 35 unit and neither is communication lost nor is everyone aboard is killed.

7: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Dave will fly into the monolith if Hall goes crazy and everyone aboard is killed; but Hal won’t go crazy.

8: Symbolize the following, using these abbreviations:

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

Communication will not be lost and Dave will not fly into the monolith only if Frank replaces the AE-35 unit and it’s not the case that both Hal goes crazy and everyone on board is killed.

9) Symbolize the statements in the following argument. Provide a dictionary indicating capital letters stand for which simple sentences.

Then use the full truth-table method to determine whether the argument is valid or invalid. Show the complete table (with a column of ‘T’s’ and ‘F’ under every operator); state explicitly whether the argument is valid or invalid; and provide a counterexample if there is one.

If the Republicans take Congress, the Obama will have to negotiate with them. But the Republicans won’t take Congress; therefore, Obama will not have to negotiate with them.

10) Use the Full truth-table method to determine whether the following argument is valid or invalid Show the complete table (with a column of ‘Ts’ and ‘Fs’ under every operator); state explicitly whether the argument form is valid or invalid; and clearly identify counterexample rows, if there are any.

(p ● q)   ̴(q v p),  p (p q)/∴  q ≡ p

11) Use the Full truth-table method to determine whether the following argument is valid or invalid Show the complete table (with a column of ‘Ts’ and ‘Fs’ under every operator); state explicitly whether the argument form is valid or invalid; and clearly identify counterexample rows, if there are any.

 (p v q)   ̴r, r ≡   ̴q /∴ q p

12) Use the Short truth-table method to determine whether the following argument form is valid or invalid show your work (T’s and F’s under as many operators-- and over as necessary) if the argument from is invalid; indicate which assignment(s) of truth-values to the variables provides a counterexample.

̴p ≡ q,   ̴r t, p ●    ̴t, s   ̴r / s q

13) Use the Short truth-table method to determine whether the following argument form is valid or invalid show your work (T’s and F’s under as many operators-- and over as necessary) if the argument from is invalid; indicate which assignment(s) of truth-values to the variables provides a counterexample.

P (r v s),   ̴ (q v t), r t, s q. /  ̴q p

Asked on by kidstudy

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

1) Communication will be lost if and only if Hal goes crazy.

If and only if is symbolized by the arrow pointing in both directions:

 `C<=> H`

2) It's not the case that both communication will be lost and Dave will fly into the monolith.

"Both" means the two statements are true at the same time, which is symbolized by the "intersection" symbol `nn` . "It's not the case" is symbolized by negation:`not`

`not (C nn D)`

3) Dave will not fly into the monolith unless Hal goes crazy.

"Unless" means "only if", so negation of D will happen only if H. If negation of D happened, this means H had had to happen as well:

`not D ->H`

4) Only if Hal goes crazy and everyone aboard is killed will Dave fly into the monolith:

`D -> (H nn E)`

5) Communication will be lost if Frank does not replace AE-35 unit, and Dave will fly into the monolith only if everyone on board is killed.

`(not F -> C) nn (D -> E)`

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The following abbreviations have been used to answer this problem:

~ : it is not the case that

& : both

V : either or

-> : if then

<--> : if and only if

H: Hal goes crazy.

E: Everyone aboard is killed.

F: Frank replaces the AE-35 unit.

D: Dave will fly into the monolith.

C: Communication: will be lost.

1. Communication will be lost if and only if Hal goes crazy.

1.s C <--> H

2. It’s not the case that both communication will be lost and Dave will fly into the monolith.

2.s ~(C&D)

3. Dave will not fly into the monolith unless Hal goes crazy.

3.s ~D<-->H

4. Only if Hal goes crazy and everyone aboard is killed will Dave fly into the monolith.

4.s D<-->(H&E)

5. Communication will be lost if Frank doesn’t replace the AE-35 unit, and Dave will fly into the monolith only if everyone on board is killed

5.s (~F->C)&(D<-->E)

6. Dave will not fly into the monolith if and only if Hal doesn’t go crazy, provided Frank replaces the AE-35 unit and neither is communication lost nor is everyone aboard is killed.

6.s (~D<-->~H)&((F&~C&~E)->~D)

7. Dave will fly into the monolith if Hall goes crazy and everyone aboard is killed; but Hal won’t go crazy.

7.s ((H&E)->(D))&~H

8. Communication will not be lost and Dave will not fly into the monolith only if Frank replaces the AE-35 unit and it’s not the case that both Hal goes crazy and everyone on board is killed.

8.s (~C&~D)<-->(F&~(H&E))

9. If the Republicans take Congress, then Obama will have to negotiate with them. But the Republicans won’t take Congress; therefore, Obama will not have to negotiate with them.

R: Republicans take Congress

N: Obama will have to negotiate with Republicans

9.s ((R->N)&~R)->~N

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