# PHI 1101 REASONING AND CRITICAL THINKING

**PHI 1101 REASONING AND CRITICAL THINKING**

PHI 1101 REASONING AND CRITICAL THINKING

PHI 1101: REASONING AND CRITICAL THINKING

INFORMATION ON TEST 3

Test 3 covers Units 12–16. The questions will be similar to those in the text, the

quizzes, and the tutorial exercises.

UNIT 12: BASIC PROPOSITIONAL LOGIC (1)

– Common propositional operators; symbolization

Operator Symbol English

Negation ¬ Not

Conjunction & And

Disjunction ∨ Or

Conditional → If . . . then

– Common forms and their symbolizations:

Both P and Q. P&Q

Not both P and Q. ¬(P&Q)

Neither P nor Q. ¬(P ∨ Q) or ¬P&¬Q

P or Q, but not both. (P ∨ Q)&¬(P&Q)

UNIT 13: BASIC PROPOSITIONAL LOGIC (2)—CONDITIONALS

– Common forms:

Statement form Symbolization(s)

If P then Q P → Q

P if Q Q → P

P only if Q P → Q or ¬Q → ¬P

P unless Q ¬Q → P

Not P unless Q ¬Q → ¬P

– Converse and contrapositive; biconditionals

– Necessary and/or sufficient conditions

– Common argument forms involving conditionals

∗ Valid

· Modus ponens: A → B, A ∴ B

· Modus tollens: A → B, ¬B ∴ ¬A

∗ Invalid

· Affirming the consequent: A → B, B ∴ A

· Denying the antecedent: A → B, ¬A ∴ ¬B

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UNIT 14: BASIC PROPOSITIONAL LOGIC (3): PROOFS

– Proofs and formal proofs

– Inference rules, a selection:

∗ Modus ponens

∗ Modus tollens

∗ Hypothetical syllogism

∗ Double negation

∗ Conjunction

∗ Simplification

∗ Weakening

∗ Disjunctive syllogism

– Proofs in propositional logic

– Proof by reduction to absurdity (not covered on Test 3)

Units 15 and 16: Inductive and causal arguments; their strengths and

weaknesses

– Inductive generalizations—factors to consider:

∗ quality of data

∗ sample size

∗ representativeness of sample

– Causal arguments: key points

∗ Correlation and causation

∗ Confusing cause and effect

∗ Common cause

∗ Post hoc fallacy

– Applications—factors to consider:

∗ Has the most specific information available about the individuals concerned been used?

∗ Has all available data been used?

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SAMPLE QUESTIONS

1. Let D=Dave will go to the store and S=Sam is out of milk. Which of the

following formulas corresponds to the statement below? (6 multiple choice

questions, 2 points each)

Dave won’t go to the store if Sam is out of milk.

(a) ¬D → S

(b) ¬(D → S)

(c) S → ¬D

(d) ¬S → ¬D

(e) ¬D → ¬S

2. Let P=Paula will go to the concert and R=Ryan will go to the concert. Which

of the following English statements corresponds to the formula below? (6 multiple choice questions, 2 points each)

¬R → ¬P

(a) Ryan won’t go to the concert if Paula doesn’t.

(b) Ryan won’t go to the concert unless Paula does.

(c) Ryan will only go to the concert if Paula does.

(d) Paula won’t go to the concert unless Ryan does.

(e) Paula will go to the concert if Ryan doesn’t.

3. State whether A is a necessary and/or a sufficient condition for B. (3 multiple

choice questions, 2 points each)

A: Being a sister; B: Having a sibling

4. Show that the following argument form is valid by constructing a proof of

its conclusion from its premises using the valid forms of inference we have

studied in this course. (You can copy and paste the symbols you see below

when typing your answer. 1 question, 4 points)

P ∨ Q, P → R, Q → S, ¬R ∴ S

(¬ & ∨ →)

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5. Discuss the strengths and weaknesses of the following arguments, which

involve inductive reasoning. (2 questions, 3 points each)

As the deadline for RRSP contributions approaches, many financial institutions advertise their investment products. Prominently

featured are the performance figures for the previous year. This is

obviously important information. For someone making a contribution, it makes sense to go with the fund that earned the most money

last year, right?

6. Discuss the strengths and weaknesses of the following argument, which

involves inductive and/or causal reasoning. (2 questions, 3 points each)

It has been documented that during the sixties and seventies, the

incidence of illicit drug use among teenagers increased in direct

proportion to the number of students who had drug education programs in the schools. Obviously, those programs served to increase

the number of teenagers using drugs.

7. Discuss the strengths and weaknesses of the following application. (2

questions, 3 points each)

I heard that your chances of winning something with this particular

lottery ticket are 1 in 6, and I’ve already bought 5 losing ones in a

row. Surely, that next one I buy will be a winner.

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