philosophy & reason · write your responses in the response book. questions 7–11 use the same...

2018 Senior External Examination

Philosophy & ReasonPaper One — Question book

Friday 2 November 20189 am to 12:10 pm

Time allowed• Perusal time: 10 minutes• Working time: 3 hours

Examination materials provided• Paper One — Question book• Paper One — Response book

Equipment allowed• QCAA-approved equipment• non-programmable calculator

DirectionsDo not write during perusal time. Paper One has three parts:

• Part A — Deductive logic (propositional logic)• Part B — Deductive logic (monadic and dyadic logic)• Part C — Critical reasoning (probability and causation)

Attempt all questions.

Suggested time allocation• Part A: 60 minutes• Part B: 70 minutes• Part C: 30 minutes

Suggested time allocation allows 20 minutes for checking responses.

AssessmentPaper One assesses the following assessment criteria:

• Knowledge• Application• Communication

Assessment standards are at the end of this book.

After the examination sessionThe supervisor will collect this book when you leave.

Planning space

1

Part A — Deductive logic (propositional logic)Part A has 15 questions. Attempt all questions.

Suggested time allocation: 60 minutes.

Section 1 — Multiple choiceSection 1 has six questions. Attempt all questions.

Each question contains four options. Select the option that you think is correct or is the best option. Respond on page 1 of the response book.

Questions 1–6 use the following dictionary.

Let: P = The proposal gets public support

F = The process is fair

B = A building permit is issued

C = Construction goes ahead

Question 1Choose the best translation of:

F ~ (B v C)

A If the process is fair, then neither is a building permit issued nor does construction go ahead.

B The process being fair is not necessary for a building permit to be issued or construction to go ahead.

C If the process is fair, then either a building permit will not be issued or construction will not go ahead.

D The process is fair only if it is not the case that both a building permit is issued and construction goes ahead.


~ C ≡ (F & ~ P)

A Construction will not go ahead, if and only if the process is fair and the proposal does not get public support.

B Construction not going ahead implies that both the process is fair and the proposal does not get public support.

C That construction does not go ahead is a necessary consequence if the process is fair and the proposal does not get public support.

D It is not the case that construction going ahead is both necessary and sufficient for the process to be fair and the proposal not to get public support.

2


~ (P & B) (~ C v ~ F)

A Without both public support for the proposal and the issue of a building permit, construction will not go ahead unless the process is not fair.

B The proposal will not get public support and a building permit will not be issued only if either construction does not go ahead or the process is not fair.

C The proposal not getting public support and a building permit not being issued are sufficient for either construction not going ahead or the process not being fair.

D It is not the case that both the proposal having public support and a building permit being issued are together sufficient for either construction not to go ahead or the process to be unfair.

Question 4Choose the best symbolisation of:

The process is fair but there is no public support for the proposal, and although a building permit is issued construction does not go ahead.

A (F v ~ P) & (B & ~ C)

B (F & ~P) & (B v ~ C)

C (F & ~ P) v (B & ~ C)

D (F & ~ P) & (B & ~ C)


Either the proposal gets public support and construction goes ahead, or a building permit is not issued, but not both.

A P & (C ~ B)

B (P & C) ~ B

C ~ ((P & C) v ~ B)

D ~ ((P & C) & ~ B)


That the proposal gets public support is not sufficient for construction to go ahead, but it is necessary.

A ~ (C P) v (P ≡ C)

B ~ (P C) v (C ≡ P)

C ~ (C P) & (P C)

D ~ (P C) & (C P)

End of Section 1

3

Section 2 — Short responseSection 2 has nine questions. Attempt all questions.

Write your responses in the response book.

Questions 7–11 use the same dictionary as Questions 1–6.

Let: P = The proposal gets public support

F = The process is fair

B = A building permit is issued

C = Construction goes ahead

Question 7Translate the following formula into meaningful English using only the dictionary provided.

C ((B F) & P)


~ (B v C) (~ P & F)

Question 9Symbolise the following into a single well-formed formula using only the dictionary provided.

Construction goes ahead even though a building permit is not issued, and the proposal gets public support even though the process is not fair.


It is not the case that both the issue of a building permit and public support for the proposal are necessary for construction to go ahead.

Question 11 Present the following argument in standard form, and symbolise it using the dictionary provided. Use the truth tree method to determine whether it is valid or invalid. If it is invalid, state a counter-example.

The proposal will either get public support, or it will not. If it gets public support and the process is fair, then a building permit will be issued. Construction will go ahead if and only if a building permit is issued. So, if the proposal does not get public support but construction goes ahead, then a building permit is issued but the process is not fair.

4

Question 12In the truth table below, the main operator is missing.

P Q (P Q) (P Q)

1 1 0

1 0 0

0 1 1

0 0 0

↑

Identify which of the following symbols could be the main operator, and explain why.

A. v

B.

C. &

D.

Note for Questions 13 and 14: Truth tables must contain clearly identified main operator columns. Responses which are not complete truth tables must contain, in every row, sufficient truth value entries to provide evidence of the reasoning supporting the main operator column values.

Question 13a. Use the truth table method to determine whether the formula below is a tautology, a contradiction or

a contingency.

(P ≡ Q) ((P & Q) v (~ P & ~ Q))

b. Confirm your response to Question 13(a) using the truth tree method.

Question 14Use the truth table method to determine whether the following argument is valid or invalid. If it is invalid, state a counter-example.

~ S (R v P)

Q ~ R

Q & ~ S

P

Question 15Evaluate the difference between statement I and statement II, including the criteria for evaluating each. You should write no more than 100 words.

I That it is raining implies that I will get wet. II It is raining, therefore I will get wet.

End of Section 2End of Part A

5

Part B — Deductive logic (monadic and dyadic logic)Part B has 12 questions. Attempt all questions.


Section 1 — Multiple choiceSection 1 has six questions. Attempt all questions.

Each question contains four options. Select the option that you think is correct or is the best option. Respond on page 1 of the response book.

Questions 1–6 use the following dictionary.

Let: Mx = x is a musician r = rock

Ix = x is an instrument j = jazz

Dx = x is a drummer m = Mark

Sx = x is a singer a = Ava

xPy = x plays y

xEy = x enjoys y


~ ( x)(~ Mx & xEj)

A No non-musicians enjoy jazz.

B No-one who is a musician enjoys jazz.

C No-one who enjoys jazz is a musician.

D It’s not the case that some musicians enjoy jazz.


( x)((Mx & Dx & Sx) xPr)

A All musicians, drummers and singers play rock.

B Only musicians who are drummers and singers play rock.

C Rock is played by all musicians, all drummers and all singers.

D Any musician who is both a drummer and a singer plays rock.

6


~ ( x)(Mx ( y)((Iy & xPy) xEy))

A Not everyone who plays an instrument that they enjoy is a musician.

B Some musicians don’t enjoy any instrument that they play.

C Not all musicians enjoy every instrument they play.

D Not all musicians play enjoyable instruments.

Question 4 Choose the best symbolisation of:

Not all who play an instrument are musicians.

A ~ ( x)( y)((Iy & xPy) Mx)

B ~ ( x)( y)((Iy & xPy) Mx)

C ~ ( x)( y)((Iy & xPy) Mx)

D ~ ( x)( y)((Iy & xPy) Mx)


All drummers play jazz, but only a few enjoy it.

A ( x)((Dx xPj) & ~ ( y)(Dy & xEy))

B ( x)(Dx & xPj) & ( x)(Dx & xEj)

C ( x)(Dx xPj) & ( x)(Dx & xEj)

D ( x)((Dx & xPj) & ( y) yEj)


Mark plays all instruments played by Ava.

A ( x)(mPx & Ix) aPx

B ( x)((Ix & mPx) & aPx)

C ( x)((Ix & aPx) mPx)

D ( x)( y)((Ix & Iy) & (aPy mPx))

End of Section 1

7

Section 2 — Short responseSection 2 has six questions. Attempt all questions.


Questions 7–11 use the same dictionary as Questions 1–6.

Let: Mx = x is a musician r = rock

Ix = x is an instrument j = jazz

Dx = x is a drummer m = Mark

Sx = x is a singer a = Ava

xPy = x plays y

xEy = x enjoys y


Sm & mPr & Ma & ( x)(aPx mEx)


( x)(Sx & ( y)( z)((Iy & (Mz & zPy)) xEy))


Ava is a singer who enjoys rock, but plays jazz.


Either any singer who plays an instrument is a musician, or not all musicians who play instruments are singers.

Question 11Symbolise the following argument using only the dictionary provided, and use the truth tree method to test it for validity. If the argument is invalid, set out as much of a counter-example as the tree provides. No test of any counter-example is required.

Ava is a musician, and she either plays an instrument or is a singer. Some singers enjoy rock, and some enjoy jazz. Any musician who plays an instrument enjoys both rock and jazz. Therefore, Ava enjoys either rock or jazz.

8

Question 12

H J K L M

a 0 1 0 0 1

b 1 1 0 1 0

Determine whether the values provided in the table form a counter-example to the argument. Set out the reasoning supporting your decision.

~ ( x)(Jx & Kx)

( x)((Hx Kx) Lx)

( x)((Mx v Hx) Kx)

End of Section 2End of Part B

9

Part C — Critical reasoning (probability and causation)Part C has three questions. Attempt all questions.



Question 1According to the most recent weather report, there is a 40% chance of rain this weekend. If it doesn’t rain, then there is an 80% chance my sailing trip will go ahead. If it does rain, there is only a 10% chance I will go sailing.

What is the probability of my going sailing this weekend?

Show your working.

Question 2A popular lottery game involves six numbers being drawn at random each week, out of a barrel containing the numbers 1 through 45. If an entrant has chosen the six numbers that are drawn, they win a large cash prize.

The lottery website displays statistical information including:

• the number of weeks since each number was last drawn

• the total number of times each number has been drawn over the past 30 years.

Evaluate the relevance of this information to prospective entrants in the lottery who are deciding which six numbers to choose.

You should write no more than 100 words.

Question 3Consider the following three statements:

A is sufficient for B.

A is necessary for B.

A is both necessary and sufficient for B.

Explain the meaning of each of these statements, using examples to illustrate your explanation. You should write no more than 100 words.

End of Part CEnd of Paper One

10 Subject – Paper One – Question/Response Book -1T:\exexams\2017\Papers\Subjects\Philosophy&Reason\standards\Philosophy & Reason Standards_P1.fm August 3, 2018 10:52 am

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philosophy & reason · write your responses in the response book. questions 7–11 use the same...

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