Chapter 9.2 & 9.3

Question 1

Since we are now dealing with compound statements whose components can be internally complex, we need a way of referring specifically to the simple components that we represent with letters. Traditionally they are called _____?

Answer 1

atomic statements, by analogy with the atoms that make up molecules.

Question 2

True or false: atomic statements do not have internal connectives

Answer 2

True

Question 3

Write the symbolic statement for the following example:

9. If the new videogame is a big seller, we will make a lot of money; but if not, we will still have learned something about the market , and we will be able to use many of the techniques we invented for other products.

Answer 3

(V horseshoe M) • [~ V horseshoe (L • I)]

Question 4

In the previous sections of chapter 9, we have defined each of the connectives in terms of a truth table. Compound statements involving these connectives are therefore “ ______ “. That is, the truth or falsity of the compound statement is a function solely of the truth values of its components and does not depend on any other connection between the components.

Answer 4

truth functional

Question 5

A statement in the form of “p • q” is ____ as long as p and q are ______ , even if those component statements have no other relationship .

Answer 5

true; both true

Question 6

we use p V q when we want to talk about ______ statements, with any pair of components

Answer 6

disjunctive

Question 7

we use p V q when we want to talk about disjunctive statements, with any pair of components. In logic we refer to the lowercase letters as ______, and to a compound formula like p V q as a ______.

Answer 7

statement variables; statement form

Question 8

modus ponens

Answer 8

affirms the antecedent

Question 9

A statement has the form if p then q.

Answer 9

conditional

Question 10

The connection between conditional statements, the if then relationship, is represented by the ___ symbol

Answer 10

“horseshoe” symbol

Question 11

A statement involving “horseshoe” connective says that if the antecedent is true, the consequent is …

Answer 11

true as well

Question 12

What is the type of statement whose connective is illustrated by the statement “if and only if” and the symbol is the “triple bar “?

Answer 12

the biconditional statement

Question 13

Use parentheses, brackets, and braces so
that the connectives __, __, __, and __ join
two components.

Answer 13

•
V
“horseshoe”
“triple bar”

Question 14

To negate a compound statement, enclose the compound statement within ______ and place the negation sign in front of the ______

Answer 14

within parentheses (or brackets)
the left parenthesis (or bracket).

Question 15

a compound statement is truth-functional because…

Answer 15

its truth or falsity is a function of the truth or falsity of its component statements

Question 16

The number of rows in a truth table are determined by….

Answer 16

2 to the nth power (nth power is the number of atomic statements; remember if an atomic statement repeats, it only counts once in the total number of atomic statements; for example, ~A • (A• B) would only be 2 to the power of 2, a total of 4 rows)

Question 17

Identify the main connective in the following statement.

(T ∨ ~E) ≡ (C • M)

Select one:

a. ⊃
b. ≡
c. •
d. ~
e. ∨

Answer 17

≡

Question 18

Identify the main connective in the following statement.

[(F ≡ L) ≡ (L ⊃ I)] • (S ∨ T)

Select one:

a. ∨
b. ~
c. ≡
d. ⊃
e. •

Answer 18

•

Question 19

Identify the correct symbolization of the following sentence, using the letters indicated in parentheses (the letters in the parentheses are in an order that corresponds to the order in which the statements appear in the sentence):

If I want to do it and I won’t harm myself or anyone else, then I should do it. (W, M, E, S)

Select one:

a. W • [~(M ∨ E) ⊃ S]
b. W • [(~M ∨ E) ⊃ S]
c. [W • (M ∨ E)] ⊃ S
d. [W • ~(M ∨ E)] ⊃ S
e. [W • (~M ∨ E)] ⊃ S

Answer 19

The correct answer is: [W • ~(M ∨ E)] ⊃ S

Question 20

Identify the main connective in the following statement.

L ⊃ [(W ⊃ L) ∨ ~(Y ⊃ T)]

Select one:

a. ≡
b. ⊃
c. ~
d. •
e. ∨

Answer 20

⊃

Question 21

Identify the main connective in the following statement.
(N ≡ T) ⊃ [(S ∨ M) • ~(H ∨ T)]

Select one:

a. ≡
b. •
c. ~
d. ⊃
e. ∨

Answer 21

⊃

Question 22

When we write out the logical form of a compound proposition, the letters p and q are used to represent:

Select one:

a. concepts
b. complete propositions
c. connectives
d. subject and predicate, respectively
e. predicate and subject, respectively

Answer 22

complete propositions

Question 23

Construct a truth table for the following statement and identify the correct set of truth values under the main connective.

(T ∨ ~E) ≡ ~T

Select one:

a. T F F F
b. F F F F
c. F T T F
d. F F F T

Answer 23

F F F T

Question 24

Construct a truth table for the following statement and identify the correct set of truth values under the main connective.

(G • N) ⊃ N

Select one:

a. T T T T
b. F F F F
c. T F T F
d. F T T T

Answer 24

T T T T

Question 25

Identify the correct symbolization of the following sentence, using the letters indicated in parentheses (the letters in the parentheses are in an order that corresponds to the order in which the statements appear in the sentence):

If you don’t believe in a God who created and designed the universe, you must believe that everything that happens and ever has happened is one vast accident. (B, H, E)

Select one:

a. B ⊃ (H ∨ E)
b. ~B ⊃ (H • E)
c. B ⊃ H • E
d. ~(B ⊃ H) • E
e. B ⊃ (H • E)

Answer 25

~B ⊃ (H • E)

Question 26

Identify the main connective in the following statement.

(D • N) ∨ G

Select one:

a. ≡
b. ~
c. •
d. ⊃
e. ∨

Answer 26

∨