Chapters 9 & 10
Modus Tollens
" in the denial mode" is also a to premise argument with one of the premises a conditional in the other premise the negation of that conditionals consequent. The conclusion is the negation of the antecedent. Ex: If P then Q Not Q Therefore not P
The phrases that go in the blanks are terms; the one that goes into the first blank as the subject term of the claim, and the one that goes into the second link is the predicate term.
"All __ are __" "No __ are __"
"Some S are not P." Which term is distributed? =P
"Some S are P." Which term is distributed? =S
translate the following claim into standard-form categorical claim. "Not every bear is a grizzly"
"Some bears are not grizzlies"
Identify the correct application of the implication (IMPL) rule
(P—>Q) —> (R v S) ~(P v Q) —> (R vS)
A syllogism is valid if, and only if, all of these conditions are met:
1. The number of negative claims in the premises must be the same as the number of negative claims in the conclusion. (because the conclusion is always one claim, this implies that no valid syllogism has two negative premises) 2. At least one premise must distribute the middle term. 3. Any term that is distributed in the conclusion of the syllogism must be distributed in its premises. ex: "all pianists are keyboard players. some keyboard players are not percussionists. some pianists are not percussionists." keyboard players is the middle term, and it is undistributed in both premises. the first premise, the A-claim, does not distribute its predicate term; the second premise, an O-claim, does not distribute its subject term. So this syllogism breaks rule 2.
How many Rosewood a truth table have if there are four letters in the symbolization
16
What is the contradictory of O
A
Conjunction
A compound claim made from to simpler claims, called conjuncts. A conjunction is true if and only if both of the simpler claims that make it up are true. ex: "Parker is at home and Moore is at work."
Categorical Logic
A system of logic based on the relations of inclusion and exclamation among categories. This branch of logic specifies the logical relationships among the claims that can be expressed in the forms "all pianists are musicians" "some politicians are not criminals"
What is the contrapositive for or apples are fruit
All non-fruit are non-apples
If Dad gets a bonus, then mom and dad will go on a vacation. How would you symbolize this claim
B—>(M&D)
A __ __ Is a syllogism who's every claim is a standard form categorical claim and in which three terms each occur exactly twice and in exactly 2 of the claims
Categorical syllogism
A __ rule allows a person to drive a conditional from two he or she already has, provided the antecedent of one of his or her conditionals is the same as the consequent of the other
Chain argument
What is the first step in finding an obverse of a claim
Change it from affirmative to negative or vice versa
Chain Argument
Comprises to conditionals for promises and another for the conclusion If P then Q If Q then R If P then R If Simone goes, then Chris will go. If Casey goes to the meeting, then Chris will go.
which of the following is an indicator word for a deductive argument
Conclusively
__ __ is both a rule and a strategy for constructing a deduction
Conditional proof
what happens when both premises of a syllogism are A- or E- claims and the conclusion is an I- or O- claim?
Diagramming the premises cannot possibly yield a diagram of the conclusion.
What is the contrary of the A claim
E
Conditional claims are sometimes spelled out in terms of necessary and sufficient conditions
Example; the presence of oxygen is a necessary condition for combustion. This tells us that we can't have combustion without oxygen, or "if we have combustion (C), then we must have oxygen (O)." Notice that the necessary condition becomes the consequence of a conditional C—>O
True or false; destructive dilemma requires the same premises as constructive dilemma
False
True or false; valid Deductive arguments fail to prove or demonstrate their conclusion
False
Identify the fallacy of denying the antecedent
If P then Q Not -P. Therefore, not -Q
Identify the pattern of modus tollens
If P then Q Not -Q/ Not-P
Equivalent Claims
If and only if in exactly the same circumstances they would both have their same truth-value. (Think of such claims as saying the same thing)
If two truth tables for two claims look exactly the same, I.E.the truth and false in one column are in the same arrangement as those in another, then these claims truth functionally __ each other
Imply
Modus Ponens
In argument consisting of a conditional claim as one premise, a claim that affirms the antecedent of the conditional as a second premise, in the claim that affirms the consequence of the conditional as the conclusion. ex: If P then Q. P, therefore Q. The generator works. The generator works only if the polarity of the cricuit has been reversed. The polarity of the cricuit has been reversed.
Identify a true statement about undistributed middle
It has the same consequent for each of its conditional premises
In the context of translating an argument into standard form, which of the following is true of the phrase "the only"?
It introduces the subject term of an A-claim
What is the term that occurs in the predicate of the syllogisms conclusion
Major
Which term occurs as the subject term of a syllogism's conclusion
Minor term
If you have a valid ID card, you can enter this office. You do have a valid ID card. Therefore, you can enter this office. What group l argument pattern does this argument take?
Modus ponens
Truth functional logic primarily concerns how claims are affected by these words
Not, and, or
What part of speech are the terms of a categorical claim?
Nouns
In the formula for determining the number of rows in a truth table, r=2(squared), what does the N Represent
Number of letters in the symbolization
What is the subcontrary claim of I?
O
Identify the rule of conjunction
P Q/ P & Q
"I will buy lunch provided that I get my paycheck" If "p" symbolizes get my paycheck; and "L" symbolizes buy lunch, How would you symbolize this claim?
P—>L
Which of the following is a legitimate case of constructive dilemma?
P—>Q R—>S P v R /:.Q v S
"All S are P. No P are Q. Therefore, no S are Q. What is the major term in this argument?
Q
Can a compound claim, the columns at the far left which set forth the rest of the table, are called __ columns
Reference
What is the second step in finding the obverse of a claim
Replace the predicate term with its complement
Identify the Rule that is broken in the syllogism. "Some pre-Colombian artifacts are Meso-American. Most meso-American artifacts are not Mayan. Therefore, some pre-Columbia's artifacts are not Mayan."
Rule 2.
What is the first step in calculating a contrapositive
Switch the places of the subject and a predicate terms
Which symbol is used to symbolize disjunction
Symbol V ("wedge")
conditional claim
The most common way of stating conditionals is by means of the words if.. then, ex:if Parker is at home, then Moore is at work.
Identify a true statement about deductive arguments
They depend on the meanings of the words that occur in their premises for the validity.
What do we call to claims that have exactly the same truth table
Truth functionally equivalent
Which type of premise should you diagram first in a Venn diagram
Universal
Before a Venn diagram is used to determine the validity of real life arguments, it helps to:
Use a letter to abbreviate each category mentioned in the argument
Is the following syllogism valid? Some S are not M All P are M Therefore some S are not P.
Valid
__ ___ graphically represents the four standard-form categorical claim types
Venn diagram
When both premises of a syllogism are A- or E- claims and the conclusion is an I- or O-claim, and if any Circle has only one area remaining on colored, a _ should be put in that area.
X
"Only birds are feather-bearing creatures." What is the equivalent claim?
all feather-bearing creatures are birds
Translate the following claim into standard form: " men are the only members of the fraternity phi delta phi."
all members of the phi delta phi are men.
"Toys are the only things on sale." Why is the translation?
all things on sale are toys
Standard form claims have subject and predicate classes that have at least one member each. This is known as:
an existential assumption
disjunction
another compound claim made up of two similar claims, called disjuncts. A disjunction is false if and only if both of its disjuncts are false. ex: " either Parker is at home, or Moore is at work."
In logic, a __ is a class or a population
category
In truth-functional logic, this is a letter that stands for a claim.
claim variable
Within the universe of discourse, the class that contains everything not in the first class is called the:
complementary class
The __ of a clean can be found by switching the positions of the subject and predicate.
converse
This concept concerns whether a claim says something about every member of the class the term names
distribution
If either the antecedent or consequent of a conditional begins with a negation sign but other does not, __ __ must be applied before contraposition can be used on it
double negation
If two claims are true and all in exactly the same circumstances, then they are __?
equivalent
If claim Q is true, what is the truth value of its negation
false
In the contacts of the square of opposition if the E claim is true the corresponding A claim is
false
True or false; some claims are not equivalent to their inverses
false
True or false; the relationships between contraries in between sub contraries are independent of existential assumptions
false
Some apples are red fruits" which type of claim is this?
i
A two premise valid argument form, one premise of which is a conditional in the other of which is the antecedent of that conditional, is known as:
modus ponens
the contradictory of a claim variable is called its
negation
Is the following a legitimate case of conjunction: P —> R /:.P—>(R & Q)
no
"Don't give peanuts to small children. Peanuts can cause an allergic reaction" which of the following is an unstated premise.
no things that can cause allergic reactions are things that you should give small children.
"No Z are Y. Some Y are Z. Therefore, some X are Z. Which rule of validity does this syllogism violate?
rule 1
All X are Y. All X are Z. Therefore all Y are Z. Which rule of validity is violated in this syllogism?
rule 3.
Which of the following rules is broken in the syllogism? " all marsupials are livebearers. No marsupials are tree-dwellers. Therefore no livebears are tree-dwellers.
rule 3.
The part of a class that is empty in a Venn diagram is indicated with shading or with an X?
shading
which is an affirmative proposition?
some humans are Carnivores
The ____ __ ___ is a diagram that concisely demonstrates the logical relationships between corresponding standard form categorical claims.
square of opposition
In the context of translating an argument into standard form, the word whenever implies that:
there is a claim about times or occasions
In a standard categorical proposition, what is the form of the verb?
to be
In a disjunction, if one disjunct is true or the other is false, the disjunction is:
true
True or false; when symbolizing a necessary condition with a conditional, the necessary condition is the consequent
true
In propositional logic, a claim is either __ or __
true or false
When symbolizing the word unless, which symbol should you use
v
Negation sign
~ In front of the P, the symbol means" change the truth value from true to false or from false to true, depending on Ps value.
which symbol is used for a conditional claim
—>
