Chapter 9 & 9.1

Question 1

Consider the following argument:

If there is a recession this year or a foreign affairs fiasco, then the president will not be reelected .
There will be a recession.
___________________________
The president will not be reelected

This is what type of argument?

Answer 1

Deductive

Question 2

In the deductive argument about the president and their reelection: the antecedent is the _______ proposition p or q, and the second premise affirms p, not the disjunction as a whole. Thus this is a combination of what two types of non-categorical syllogisms?

Answer 2

disjunctive; a combination of both disjunctive and hypothetical syllogisms

Question 3

_________ logic is one main branch of what is known as symbolic logic.

Answer 3

Propositional

Question 4

Propositional logic is a branch of what type of logic?

Answer 4

Symbolic

Question 5

In modern ______ logic, words like “all,” “some,” “if … then ,” and “or” are replaced with symbols.

Answer 5

Symbolic

Question 6

Propositional logic is the logic of _____ statements - statements that are made up of other, simpler propositions.

Answer 6

Compound

Question 7

Here are some examples _______ statements:
1. My sister is happy, and she’s throwing a party.
2. My brother is not coming to the party.
3. The Democrats will win or the Republicans will win.
4. If the Democrats win, then my sister will be happy.
5. The party will be fun if and only if Buzz shows up.

Each of these statements has one or more component statements with an italicized expression, called a connective , which tells us how the components are related

Answer 7

Compound

Question 8

In symbolic logic, a _______ proposition, or statement, is called a conditional statement.

Answer 8

Hypothetical, because of its dependence on the events taking place in the premise

Question 9

In the state statement “The party will be fun if and only if Aaron shows up,” the connective “if and only if “ is called a ________.

Answer 9

biconditional

Question 10

A ______ is a way of expressing two component statements, called _____ , in a single statement .

For example:
6. The rent is due, and I have no money.

Answer 10

conjunction | conjuncts

Question 11

Consider the following statement:
The rent is due, and I have no money.

For it to be true, both ______ must be true. And if they are both true, the _____ is true.

Answer 11

conjuncts | conjunction

Question 12

The conjunction sign ____ represents the relationship

between the truth of components and the truth of a compound statement as a whole.

Answer 12

• (called the “dot”)

Question 13

The logical form of a conjunction is…

Answer 13

p • q

Question 14

The letters “p” and “q” stand for the two component statements, and each of those components can be either true or false. The truth or falsity of any statement is
called its ____, represented by T and F.

Answer 14

truth value

Question 15

The statement
“Lemons are fruit” has the _____ value of T

While the statement
“Lemons grow in the Arctic” has the ____ value F.

Answer 15

truth value

Question 16

Consider the following statements:

10. Renee and Tom took logic.
11. Tony and Sue got married.

Statement 10 is a normal conjunction: It is shorthand for “Renee took logic and Tom took logic.” But 11 is different. Why?

Answer 16

It does not mean merely that Tony got married (to
someone) and chat Sue also got married (to someone). It means that Tony and Sue got married to each other.

So the sentence makes a single statement about a pair of people; it is not a pair of statements that can be joined by conjunction or represented by the truth table for the dot.

Question 17

When discussing negation we represent the denial of a proposition by what sign?

Answer 17

the negation sign called the “tilde” or represented by “ ~ “ symbol

Question 18

T and ~T are contradictory propositions, meaning….

Answer 18

they cannot both be true, and they cannot both be false.

Question 19

T and ~T are ______ propositions, meaning they cannot both be true, and they cannot both be false.

Answer 19

contradictory propositions

Question 20

In the following statement what would be the symbolic representation of the double negative?

It’s not the case that Larry will not come.

Answer 20

~~L

which essentially means Larry will come. Negation is an on / off switch; flip it twice and you ‘re back where you started.

Question 21

A _____ statement asserts that either p or q is true.

Answer 21

disjunctive

Question 22

disjunctive statement (in symbolic logic)

Answer 22

asserts that either p or q is true (so at least one component must be true, or can also mean both)

Question 23

in a disjunctive statement, p and q are called the disjuncts, and the connective “or” is represented by what symbol?

Answer 23

V

the “vee” or “wedge” sign

Question 24

in symbolic logic the connective “___” is represented by V (the “vee” or “wedge” sign).

Answer 24

“or”

Question 25

What is the symbolic form of the following disjunctive statement:

We will grow corn in our field or we will let it lie fallow.

Answer 25

G V L

Question 26

What is the symbolic form of the following disjunctive statement:

Chelsea got a job with Goldman Sachs or Morgan Stanley.

Answer 26

C V J

Question 27

What is the symbolic form of the following disjunctive statement:

Either the Yankees or the Twins will win the American League pennant.

Answer 27

Y V T

Question 28

A ____ statement has the form “if p then q.” (synonymous with hypothetical syllogism). In such a statement “p” is called the antecedent and “q” the consequent.

Answer 28

conditional

Question 29

In symbolic logic a _____ statement, “if p then q,” is synonymous with hypothetical syllogism. In such a statement “p” is called the _____ and “q” the ______.

Answer 29

conditional
p = antecedent
q = consequent

Question 30

in a conditional statement the connection between the antecedent and consequent (if then relationship) is represented by what symbol?

Answer 30

“horseshoe”

Question 31

In statement where the horseshoe symbol is used as a connective, it represents that….

Answer 31

if the antecedent is true, the consequent is true
as well. it does not assert that the each are true, but what it does assert is that there’s a relationship between the two.

Question 32

What is the symbolic notation for the following statement:

If you study hard, you will pass the test.

Answer 32

S “horseshoe” P

Question 33

What is the symbolic notation for the following statement:

If the Jet Stream shifts to the north, there will be drought in the Midwest.

Answer 33

J “horseshoe” D

Question 34

What is the symbolic notation for the following statement:

If the city imposes rent control, there will be a housing shortage.

Answer 34

R “horseshoe” S

Question 35

A conditional statement means there is a ____ amongst the components.

Answer 35

dependence

Question 36

Conditional Statement

Answer 36

has the form “if p then q.” (synonymous with hypothetical syllogism) and shows the dependence of components.

Question 37

In conditional statements (ch. 8 where we called them hypothetical statements), we noted that if p then q is not equivalent to if q then p, and neither one implies the other.

For example, suppose we reverse the antecedent and consequent in statement 19:

19. If the city imposes rent control, there will be a housing shortage. R :::> H

19’. If there is a housing shortage, the city has imposed rent controls. H :::> R

What do the statements mean when the order is flipped?

Answer 37

Statement 19 states that rent control will result in a housing shortage. It does not state that rent controls are the only cause of shortages. But that’s exactly what 19’ says. If a shortage occurs in the absence of rent controls, 19’ is false, but 19 may still be true.

Question 38

The following are examples of what kind of statements?

21a. I will go camping this weekend if I finish my work.
21 b. I will go camping this weekend only if I finish my work.
21 c. I will go camping this weekend unless it rains.

Answer 38

Conditional

Question 39

Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?

p if q

Answer 39

If q, then p
_____________
q “horseshoe” p

Question 40

Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?

p only if q

Answer 40

If p then q
_____________
p “horseshoe” q

Question 41

Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?

p unless q

Answer 41

If not-q, then p
______________
~q “horseshoe” p

and

If not-p, then q
______________
~p “horseshoe” q

Question 42

biconditional statements take the form of “if and only if” and are illustrated by what symbol?

Answer 42

a “triple bar “

≡

Question 43

_______statements take the form of “if and only if” and are illustrated by a “triple bar” ≡ symbol

Answer 43

biconditional

Question 44

What is the symbolic notation for the following statement?

I will teach the class if and only if 10 or more students enroll

Answer 44

T ≡ E

Question 45

in what type of statement are there two dependent statements: one of them is indicated by the “if” and the other by the “only if”

Answer 45

biconditional

Question 46

We typically use the _______ to state:
• A “go/ no go” criterion for an action or a decision
• The criteria for inclusion in a category
• The terms of a contract
• The causal factors governing an event

Answer 46

biconditional, “if and only if”

Question 47

What is the standard truth value of a biconditional statement?

Answer 47

A biconditional statement is true when the two components have identical truth values ; they are either both true or both false.

Question 48

The statement form p ≡ q is:

Select one:

a. a conjunction
b. a disjunction
c. not actually a statement form
d. a biconditional
e. a negation

Answer 48

The correct answer is: a biconditional

Question 49

The connective “≡” is called:

Select one:

a. “horseshoe”
b. “triple bar”
c. “wedge”
d. “dot”
e. “tilde”

Answer 49

The correct answer is: “triple bar”

Question 50

The statement form p = q is:

Select one:

a. a disjunction
b. a biconditional
c. a conjunction
d. a conditional
e. not actually a statement form

Answer 50

The correct answer is: not actually a statement form

Question 51

Choose which symbol to use for “just in case” and “just in the event that.”

Select one:

a. ~
b. ⊃
c. •
d. ≡
e. ∨

Answer 51

The correct answer is: ≡

Question 52

The statement form ~p is:

Select one:

a. a conditional
b. a negation
c. not actually a statement form
d. a conjunction
e. a disjunction

Answer 52

The correct answer is: a negation

Question 53

The connective used for disjunctions is:

Select one:

a. ⊃
b. ∨
c. •
d. ~
e. ≡

Answer 53

The correct answer is: ∨

Question 54

The connective used for biconditionals is:

Select one:

a. ≡
b. •
c. ⊃
d. ∨
e. ~

Answer 54

The correct answer is: ≡

Question 55

Identify which of the following is a correct symbolization of the following statement.

  If you say it cannot be done, you should not interrupt the one doing it.

Select one:

a. ~S ≡ ~I
b. ~S ⊃ ~I
c. S • ~I
d. ~S ∨ ~I
e. ~S • ~I

Answer 55

The “If” clearly indicates this statement is a conditional.

The phrase (antecedent) “you say it cannot be done” is equivalent to “you don’t say it can be done” and is symbolized as ~S.

(As a side point, suppose it were “you don’t say it cannot be done” (which is a double negative), that would be equivalent to “you say it can be done” – and both would be symbolized as simply S. Also, note that the statement is not literally claiming that someone says or utters, or doesn’t say or utter, something; if that were the case, it should be written as so: you don’t say “it cannot be done…” Similar remarks apply to the original phrase.)

The correct answer is: ~S ⊃ ~I

Question 56

The statement form p ⊃ q is:

Select one:

a. a conjunction
b. not actually a statement form
c. a conditional
d. a disjunction
e. a negation

Answer 56

The correct answer is: a conditional

Question 57

Complete the passage below.

Logical connectives are defined in terms of truth tables. Compound statements involving connectives are therefore…

Select one:

a. …truthful.
b. …truth-like.
c. …truth-functional.
d. …truth-oriented.
e. …relatively true.

Answer 57

The correct answer is: …truth-functional.

Question 58

A _____ asserts that either p or q is true.

Answer 58

disjunctive statement

Question 59

The component statements p and q are called the_____ in a _____ statement and the connective “or” is represented by V —the “vee” or “wedge” sign.

Answer 59

disjuncts in a disjunctive statement

Question 60

_______ statements, which are also called contrary-to fact or counterfactual statements, are not truth-functional
and can’t be symbolized by the “horseshoe” symbol.

Answer 60

Subjunctive

Question 61

Subjunctive statements, which are also called ______ or _______ statements, are not truth-functional and can’t be symbolized by the “horseshoe” symbol.

Answer 61

contrary-to fact or counterfactual

Question 62

With the following subjunctive statement: Squirrels eat nuts if and only if London has a subway is true because both components are _____. The lack of any connection in this case is
irrelevant.

Answer 62

true

symbolic representation of this statement is:
S ≡ L

Question 63

With the following subjunctive statement: Tom Clancy wrote Hamlet if and only if triangles have four sides is true because both components are ______ . The lack of any connection in this case is
irrelevant.

Answer 63

false

symbolic representation of this statement is:
C ≡ T

Question 64

With the following subjunctive statement:
I would have won the Olympic marathon if and only if I had had Wheaties every morning for breakfast.

is clearly _____ even though both components have the same truth value (false).

Answer 64

False