Chapter 9.4-10.2

Question 1

We have learned that connectives are truth-functional, meaning….

Answer 1

The truth or falsity of a compound statement is determined solely by the truth values of its atomic components; for each combination of those truth values , the connectives specify whether the compound statement is true or false

Question 2

________ determine the logical form of a statement, and we have seen how statements with the same logical form have certain features in common.

Answer 2

Connectives

Question 3

Connectives determine…

Answer 3

the logical form of a statement, and we have seen how statements with the same logical form have certain features in common.

Question 4

In a truth table for a compound statement, each row represents a specific combination of truth values for the ______ , and the rows taken together represent _______.

Answer 4

atomic statements;

every possible combination of atomic truth values.

Question 5

In the statement A ≡ A, the statement has to be _____ by the very nature of it having a biconditional connective (≡), regardless of what statement says.

Answer 5

True

Question 6

In the statement

The Empire State Building has 97 floors if and only if the Empire State Building has 97 floors.

is true. A statement that has this property is called a ______.

Answer 6

tautology

Question 7

A tautology is a compound statement that is….

Answer 7

true for every combination of truth values of its atomic components. In the truth table for a tautology, therefore, the column under the main connective will have only T’s, no F’s.

Question 8

In a truth table for a _____ the column under the main connective will have only T’s, and there are no F’s.

Answer 8

tautology

Question 9

By the very nature of _______, A and ~A cannot both be true, therefore such a statement contradicts itself. Statement A may be true or it may be false, but A • ~A has to be false.

Answer 9

negation

Question 10

In the statement:

Vinegar is an acid and vinegar is not an acid

the statement is false. Statements that have this property are called _________.

Answer 10

self-contradictions

Question 11

In the truth table for a self-contradiction, the column

under the main connective will have only __’s, no __’s.

Answer 11

Only F’s and no T’s

Question 12

Compound statements that are neither tautologies nor self-contradictions are called ______ statements (or_____).

Answer 12

contingent statements

contingencies

Question 13

_______ statements are true for some combinations of atomic truth values, false for others.

Answer 13

Contingent

Their truth value, in other words, is contingent on the truth or falsity of their atomic components as well as their logical form, so they are true on some rows of their truth table but false on others.

Question 14

Truth tables can also reveal certain relationships between compound statements, like equivalence.

Two statements are equivalent when …

Answer 14

they have exactly the same truth values on each row of their respective truth tables (i.e., the same
truth values in the column under their main connectives).

Question 15

in terms of ________: p ⊃ q is the same as ~p V q because when it is written into a truth value table the main connectives of the two statements have the same exact set of truth values, and thus the above statements are ________.

Answer 15

equivalence;

equivalent

Question 16

in terms of ________: ~ (p • q) is the same as ~p V ~q because when it is written into a truth value table the main connectives of the two statements have the same exact set of truth values, and thus the above statements are ________.

Answer 16

equivalence;

equivalent

Question 17

The opposite relationship to equivalence is _____. Two statements are _____ when they have opposite values on every row of their respective truth tables (i.e., opposite truth values on each row under their main connectives)

Answer 17

contradiction;

contradictory

Question 18

Tautology and self-contradiction are features of ____

statements, whereas equivalence and contradiction are relationships between statements.

Answer 18

individual;

two

Question 19

Like equivalence and contradiction, these are relationships that hold in virtue of the logical forms of the statements involved. Two statement forms are _______ if it is possible for instances of those forms to both be true.

Answer 19

consistent

Question 20

For statements to be consistent, there must be ____ row on which both statements are true.

Answer 20

at least one row

Question 21

criterion for consistency is not merely that the statements have the same truth value on at least one row, but that that value be ____.

Answer 21

T

Question 22

criterion for _______ is not merely that the statements have the same truth value on at least one row, but that that value be T.

Answer 22

consistency

Question 23

_____ and _____ are relationships that apply not only to pairs of statement forms but to sets of three or more.

Answer 23

consistency;

inconsistency