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Philosophy, Coursework

Intro to Logic Exam

Intro to Logic Exam

Question 1.

Translate the English sentences below into symbolic logic.

Remember to use the arrow symbol -> for conditional sentences. Make sure you do not confuse the antecedent with the consequent.

Please use these specified letters for the following atomic sentences:

Use the letter – C (negation of C) for “Nothing changes” and the letter T for “Time is passing”.

  1. If nothing changes, then there is no time passing. -C -> -T
  2. * (In this example use also the letter M for “Time is a measure of change.”)

If time is a measure of change then if nothing changes there is no time passing. M -> -(C -> T)

  1. If time is a measure of change, then there is no time passing unless there is change. M -> -(C -> T)
  2. If nothing changes then there is no time passing, if time is a measure of change. M -> -(C -> T)
  3. I will go jogging, unless it rains. -R -> J

Question 2.

First translate the arguments below into symbols, then determine if the argument is valid or invalid. For valid arguments, say what method of inference was used (for example: MP, MT, DS, HS….). For invalid arguments, say what logical fallacy the argument represents.

  2. If someone voted for Trump, then that person is a Trump supporter.
  3. Jack is a Trump supporter.
  4.  So Jack voted for Trump.

Valid or Invalid? ____Invalid____

Here write your translation:

*Make sure I will understand what your letters stand for. Avoid using X, Y, Z.   You can use for example V for the part about voting, and S for the part about being a supporter.

  1. V -> S
  2. S
  3. V

The conclusion is invalid because Jack being a supporter of Trump does not necessarily mean he voted for Trump.

  1. b)
  2. If a person is pregnant, then that person is a female.
  3. Sam is a female.
  4. Therefore, Sam is pregnant.

Valid or Invalid? ____Invalid____

Here write your translation:

  1. P -> F
  2. F
  3. P

Sam is a female, but it does not necessarily mean she is pregnant.

c)

  1. If a person is pregnant, then that person is not a male.
  2. But Sam is definitely not a male.
  3. So, Sam is not pregnant.

Valid or Invalid? ___Valid_____

Here write your translation:

  1. P -> -M
  2. –M
  3. –P MT

d)

  1. Sam is a female, if Sam is pregnant.
  2. But Sam is not pregnant.
  3. Therefore, Sam is not a female.

Valid or Invalid? ___Invalid_____

Here your translation:

  1. P -> F
  2. –P
  3. –F

Premise two does not follow the first premise; therefore, the conclusion is invalid. More so, Sam not being pregnant does not necessarily mean Sam is not a female.

  1. e)
  2. If Jack voted for Trump, then Jack is a Trump supporter.
  3. Turns out Jack did not vote for Trump.
  4. So Jack is not a Trump supporter.

Valid or Invalid? ___Invalid____

Here your translation:

  1. V-> S
  2. –V
  3. –S

The argument is invalid reasoning since the second premise does not follow the first, making the conclusion invalid. Jack not voting for Trump does not necessarily mean he does not support Trump.

f)

  1. If one voted in the presidential election in the US, then one is a US citizen.
  2. Jack is not a US citizen.
  3. Therefore, Jack did not vote in the presidential election in the US.

Valid or Invalid? ____valid____

Here your translation:

  1. V -> C
  2. –C
  3. –V MT

g)

  1. If a given number’s factors add up to the original number, then that number is called a perfect number.
  2. The factors of 6, that is 1, 2, and 3, add up to 6.
  3. Therefore, 6 is a perfect number.

Valid or Invalid? ____Valid____

Here write your translation:

  1. F -> P
  2. F
  3. P MP

h)

  1. If Sam is pregnant, then Sam is either a female or not a male.
  2. But it’s not true that Sam is either a female or not a male.
  3. Therefore, Sam is not pregnant.

Valid or Invalid? ____Valid____

Here your translation:

  1. P -> (F v -M)
  2. – (F v -M)
  3. –P MT

i)

  1. If you are on the Borneo island, then you are either in Indonesia in the south, or in the north in Malaysia or Brunei.
  2. Eva is indeed on the Borneo island right now.
  3. But Eva is not in Indonesia in the south.
  4. So Eva is in either in Malaysia or Brunei.

Valid or Invalid? _____Valid___

Here your translation:

  1. I -> (S v M v B)
  2. I
  3. –S
  4. M v B DS

Question 3.

Write a conclusion that follows logically from the given premises.   Make sure you say what method of inference you used.

  2. A -> B
  3. B -> C

__________

  1. A -> C    HS
  3. N -> O
  4. (L v M)-> N
  5. – O

____________

  1. 4. (L v M) -> O    HS
  2. –(L v M) MT
  4. – A -> – ( M v L)
  5. ( M v L)
  6. – W
  7. A -> (K v W)

_____________

  1.   A
  2. A -> -W MT
  3. A -> K MP

 

  1. ( N v M) -> U
  2. – U

_____________

  1. –(N v M)     MT
  3. – N -> – ( B v Q)
  4. – U -> – N

__________

  1. – U -> – (B v Q)

     

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    Question 

Intro to Logic Exam

Your Name: ____________________________________________

Instructions:

Answer all questions by yourself.  Plagiarized answers will get you an F for the exam.  (Plagiarism includes submitting answers that someone else wrote for you.)

Question 1.

Translate the English sentences below into symbolic logic.

Remember to use the arrow symbol -> for conditional sentences. Make sure you do not confuse the antecedent with the consequent.

Intro to Logic Exam

Intro to Logic Exam

Please use these specified letters for the following atomic sentences:

Use the letter – C (negation of C) for “Nothing changes” and the letter T for “Time is passing”.

If nothing changes, then there is no time passing.

b)

* (In this example use also the letter M for “Time is a measure of change.”)

If time is a measure of change then if nothing changes there is no time passing.

c)

If time is a measure of change, then there is no time passing unless there is change.

d)

If nothing changes then there is no time passing, if time is a measure of change.

  1. e)

I will go jogging, unless it rains.

Question 2.

First translate the arguments below into symbols, then determine if the argument is valid or invalid.  For valid arguments, say what method of inference was used (for example: MP, MT, DS, HS….).  For invalid arguments, say what logical fallacy the argument represents.

  2. If someone voted for Trump, then that person is a Trump supporter.
  3. Jack is a Trump supporter.

_____________

  1. So Jack voted for Trump.

Valid or Invalid? ________

Here write your translation:

*Make sure I will understand what your letters stand for.  Avoid using X, Y, Z.   You can use for example V for the part about voting, and S for the part about being a supporter.

1.

2.

_____

3.

  1. b)
  2. If a person is pregnant, then that person is a female.
  3. Sam is a female.

____________________

  1. Therefore, Sam is pregnant.

Valid or Invalid? ________

Here write your translation:

1.

2.

_____

3.

  1. c)
  2. If a person is pregnant, then that person is not a male.
  3. But Sam is definitely not a male.

____________________

  1. So, Sam is not pregnant.

Valid or Invalid? ________

Here write your translation:

1.

2.

_____

3.

d)

  1. Sam is a female, if Sam is pregnant.
  2. But Sam is not pregnant.

____________________

  1. Therefore, Sam is not a female.

Valid or Invalid? ________

Here your translation:

1.

2.

_____

3.

  1. e)
  2. If Jack voted for Trump, then Jack is a Trump supporter.
  3. Turns out Jack did not vote for Trump.

_____________

  1. So Jack is not a Trump supporter.

Valid or Invalid? ________

Here your translation:

1.

2.

_____

3.

  1. f)
  2. If one voted in the presidential election in the US, then one is a US citizen.
  3. Jack is not a US citizen.

_______________

  1. Therefore, Jack did not vote in the presidential election in the US.

Valid or Invalid? ________

Here your translation:

1.

2.

_____

3.

g)

  1. If a given number’s factors add up to the original number, then that number is called a perfect number.
  2. The factors of 6, that is 1, 2, and 3, add up to 6.

_______________

  1. Therefore, 6 is a perfect number.

Valid or Invalid? ________

Here write your translation:

1.

2.

_____

3.

  1. h)
  2. If Sam is pregnant, then Sam is either a female or not a male.
  3. But it’s not true that Sam is either a female or not a male.

____________________

  1. Therefore, Sam is not pregnant.

Valid or Invalid? ________

Here your translation:

1.

2.

_____

3.

i)

  1. If you are on the Borneo island, then you are either in Indonesia in the south, or in the north in Malaysia or Brunei.
  2. Eva is indeed on the Borneo island right now.
  3. But Eva is not in Indonesia in the south.

__________________

  1. So Eva is in either in Malaysia or Brunei.

Valid or Invalid? ________

Here your translation:

1.

2.

3.

____

4.

Question 3.

Write a conclusion that follows logically from the given premises.   Make sure you say what method of inference you used.

  2. A -> B
  3. B -> C

__________

  3. N -> O
  4. (L v M)-> N
  5. – O

_____________

4.

5.

  2. – A -> – ( M v L)
  3. ( M v L)
  4. – W
  5. A -> (K v W)

_____________

  5.   ( N v M) -> U
  6. – U

_____________

  3. – N -> – ( B v Q)
  4. – U -> – N

__________

3.

Notes:

PLEASE READ AND ANSWER QUESTIONS CAREFULLY. EVERYTHING HAS TO BE ANSWERED STRAIGHT ON THE DOCUMENT. NO PLAGIARISM EVERYTHING IN OWN WORDS.

 

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