Chapter 9 & 9.1 Flashcards
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?
Deductive
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?
disjunctive; a combination of both disjunctive and hypothetical syllogisms
_________ logic is one main branch of what is known as symbolic logic.
Propositional
Propositional logic is a branch of what type of logic?
Symbolic
In modern ______ logic, words like “all,” “some,” “if … then ,” and “or” are replaced with symbols.
Symbolic
Propositional logic is the logic of _____ statements - statements that are made up of other, simpler propositions.
Compound
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
Compound
In symbolic logic, a _______ proposition, or statement, is called a conditional statement.
Hypothetical, because of its dependence on the events taking place in the premise
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 ________.
biconditional
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.
conjunction | conjuncts
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.
conjuncts | conjunction
The conjunction sign ____ represents the relationship
between the truth of components and the truth of a compound statement as a whole.
• (called the “dot”)
The logical form of a conjunction is…
p • q
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.
truth value
The statement
“Lemons are fruit” has the _____ value of T
While the statement
“Lemons grow in the Arctic” has the ____ value F.
truth value
Consider the following statements:
- Renee and Tom took logic.
- 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?
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.
When discussing negation we represent the denial of a proposition by what sign?
the negation sign called the “tilde” or represented by “ ~ “ symbol
T and ~T are contradictory propositions, meaning….
they cannot both be true, and they cannot both be false.
T and ~T are ______ propositions, meaning they cannot both be true, and they cannot both be false.
contradictory propositions
In the following statement what would be the symbolic representation of the double negative?
It’s not the case that Larry will not come.
~~L
which essentially means Larry will come. Negation is an on / off switch; flip it twice and you ‘re back where you started.
A _____ statement asserts that either p or q is true.
disjunctive
disjunctive statement (in symbolic logic)
asserts that either p or q is true (so at least one component must be true, or can also mean both)
in a disjunctive statement, p and q are called the disjuncts, and the connective “or” is represented by what symbol?
V
the “vee” or “wedge” sign
in symbolic logic the connective “___” is represented by V (the “vee” or “wedge” sign).
“or”
What is the symbolic form of the following disjunctive statement:
We will grow corn in our field or we will let it lie fallow.
G V L
What is the symbolic form of the following disjunctive statement:
Chelsea got a job with Goldman Sachs or Morgan Stanley.
C V J
What is the symbolic form of the following disjunctive statement:
Either the Yankees or the Twins will win the American League pennant.
Y V T
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.
conditional
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 ______.
conditional
p = antecedent
q = consequent
in a conditional statement the connection between the antecedent and consequent (if then relationship) is represented by what symbol?
“horseshoe”
In statement where the horseshoe symbol is used as a connective, it represents that….
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.
What is the symbolic notation for the following statement:
If you study hard, you will pass the test.
S “horseshoe” P
What is the symbolic notation for the following statement:
If the Jet Stream shifts to the north, there will be drought in the Midwest.
J “horseshoe” D
What is the symbolic notation for the following statement:
If the city imposes rent control, there will be a housing shortage.
R “horseshoe” S
A conditional statement means there is a ____ amongst the components.
dependence
Conditional Statement
has the form “if p then q.” (synonymous with hypothetical syllogism) and shows the dependence of components.
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:
- 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?
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.
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.
Conditional
Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?
p if q
If q, then p
_____________
q “horseshoe” p
Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?
p only if q
If p then q
_____________
p “horseshoe” q
Conditional statements can be put into standard form. How would the following non standard form be converted to standard form?
p unless q
If not-q, then p
______________
~q “horseshoe” p
and
If not-p, then q
______________
~p “horseshoe” q
biconditional statements take the form of “if and only if” and are illustrated by what symbol?
a “triple bar “
≡
_______statements take the form of “if and only if” and are illustrated by a “triple bar” ≡ symbol
biconditional
What is the symbolic notation for the following statement?
I will teach the class if and only if 10 or more students enroll
T ≡ E
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”
biconditional
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
biconditional, “if and only if”
What is the standard truth value of a biconditional statement?
A biconditional statement is true when the two components have identical truth values ; they are either both true or both false.
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
The correct answer is: a biconditional
The connective “≡” is called:
Select one:
a. “horseshoe”
b. “triple bar”
c. “wedge”
d. “dot”
e. “tilde”
The correct answer is: “triple bar”
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
The correct answer is: not actually a statement form
Choose which symbol to use for “just in case” and “just in the event that.”
Select one:
a. ~
b. ⊃
c. •
d. ≡
e. ∨
The correct answer is: ≡
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
The correct answer is: a negation
The connective used for disjunctions is:
Select one:
a. ⊃
b. ∨
c. •
d. ~
e. ≡
The correct answer is: ∨
The connective used for biconditionals is:
Select one:
a. ≡
b. •
c. ⊃
d. ∨
e. ~
The correct answer is: ≡
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
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
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
The correct answer is: a conditional
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.
The correct answer is: …truth-functional.
A _____ asserts that either p or q is true.
disjunctive statement
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.
disjuncts in a disjunctive statement
_______ statements, which are also called contrary-to fact or counterfactual statements, are not truth-functional
and can’t be symbolized by the “horseshoe” symbol.
Subjunctive
Subjunctive statements, which are also called ______ or _______ statements, are not truth-functional and can’t be symbolized by the “horseshoe” symbol.
contrary-to fact or counterfactual
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.
true
symbolic representation of this statement is:
S ≡ L
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.
false
symbolic representation of this statement is:
C ≡ T
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).
False