Deck 7: Statement Logic: Truth Tables

Question 1

In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?

A) the first occurrence of ⋁
B) •
C) →
D) the second occurrence of ⋁

Answer 1

→

Question 2

Which of the following is an atomic statement?

A) Sailing is an enjoyable sport.
B) Sewing and cross-stitch require good eyesight.
C) The Cincinnati Reds did not win their last game.
D) Either Sue or Karen will get the high score.

Answer 2

Sailing is an enjoyable sport.

Question 3

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Neither Fred nor Lou likes ice cream" is best symbolized by

A) ~F ⋁ ~L.
B) ~F • ~L.
C) ~F → ~L.
D) ~(F • L)

Answer 3

~F • ~L.

Question 4

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Either Fred or Lou doesn't like ice cream" is best symbolized by

A) ~F ⋁ ~L.
B) ~F • ~L.
C) ~F → ~L.
D) ~(F • L).

Question 5

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Fred doesn't like ice cream only if Lou doesn't like ice cream" is best symbolized by

A) ~F ⋁ ~L.
B) ~F • ~L.
C) ~F → ~L.
D) ~(F • L).

Question 6

The "⋁" sign is used to symbolize

A) "Either . . . or . . . but not both."
B) "If . . . then . . ."
C) "Both . . . and . . ."
D) "Either . . . or . . . or both."

Question 7

In A → B,

A) A provides a necessary condition for B.
B)B provides a sufficient condition for A.
C) A provides a sufficient condition for B.
D) A provides both a necessary and sufficient condition for B.

Question 8

Which of the following is not a condition for a symbolic expression to be a well-formed formula (WFF)?

A) If p is a WFF, then so is ~(p).
B) If p and q are WFFs, then so is (p • q).
C) If p and q are WFFs, then so is (p ⋁ q).
D) If p and q are WFFs, then so is (p → q).

Question 9

Which of the following is not a well-formed formula (WFF)?

A) (~A→B⋁C)
B) ~A→(B⋁C)
C) ~(A→B)⋁C
D) (~A→B)⋁C

Question 10

A compound statement is truth-functional if

A) more than one atomic statement is a component.
B) its truth value is a function of the content of its component atomic statement(s).
C) in most contexts it functions as a true statement.
D) its truth value is a function of the truth value of its component atomic statements.

Question 11

On which assignment of truth values does the sentence A → ~B turn out to be false?

A) A is true, and B is true.
B) A is true, and B is false.
C) A is false, and B is true.
D) A is false, and B is false.

Question 12

Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?

A) A is true, B is false, and C is false.
B) A is false, B is true, and C is false.
C) A is false, B is false, and C is false.
D) A is true, B is false, and C is true.

Question 13

Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true?

A) A is true, B is false, and C is false.
B) A is true, B is true, and C is false.
C) A is false, B is false, and C is false.
D) A is true, B is false, and C is true.

Question 14

The truth table for a symbolized argument containing four statement letters will have

A) 4 rows.
B) 8 rows.
C) 12 rows.
D) 16 rows.

Question 15

Using a truth table, we can tell that an argument is valid if

A) there is at least one row where the premises and conclusion are all true.
B) there is no row where the premises are true and the conclusion is false.
C) there is no row where the conclusion is false.
D) there is at least one row where the premises are all true and the conclusion is false.

Question 16

A compound statement is a tautology if

A) it is false regardless of the truth values assigned to the atomic sentences that compose it.
B) its truth value is a function of the truth values of its component atomic sentences.
C) it is true regardless of the truth values assigned to its component atomic sentences.
D) its truth value is a function of the placement of its parentheses.

Question 17

A compound statement is a contradiction if

A) it is false regardless of the truth values assigned to the atomic sentences that compose it.
B) its truth value is a function of the truth values of its component atomic sentences.
C) it is true regardless of the truth values assigned to its component atomic sentences.
D) its truth value is a function of the placement of its parentheses.

Question 18

When two statements are logically equivalent, the columns in the truth table under their main logical operators

A) show neither statement is contingent.
B) are exactly alike.
C) are exactly opposite.
D) show both statements are tautologies.

Question 19

An atomic statement is a statement that has no other statement as a component.

Question 20

A compound statement is one that has at least one atomic statement as a component.

Question 21

"Chocolate is not nutritious" is an atomic statement.

Question 22

"All roses are red flowers" is a compound statement.

Question 23

In A • B, the statement constants are called disjuncts.

Question 24

The symbol for disjunction represents inclusive "or."

Question 25

In A → B, the consequent is B.

Question 26

The statement ~A ⋁ B is a negation.

Question 27

A sufficient condition is a condition that, if lacking, guarantees that a statement is false (or that a phenomenon will not occur).

Question 28

A necessary condition is a condition that guarantees that a statement is

Question 29

The consequent of a

Question 30

The English phrase "if and only if" is symbolized with the "↔".

Question 31

A statement variable is a lower case letter that serves as a placeholder for any statement.

Question 32

(A → B ⋁ C) is a well-formed formula.

Question 33

(A → (B ⋁ C) ⋁ D) is a well-formed formula.

Question 34

In A ⋁ (B • C), the main logical operator is the "⋁".

Question 35

In (A ⋁ (B) • (D ⋁ C), the main logical operator is the "⋁".

Question 36

A compound statement is truth functional if its truth value is completely determined by the truth value of the atomic statements that compose it.

Question 37

A conjunction is .

Question 38

A disjunction is false if both its disjuncts are false; otherwise it is

Question 39

A material conditional is false if its antecedent is ; otherwise, it is

Question 40

A material biconditional is

Question 41

An argument is valid when it is not possible for its conclusion to be false when all of its premises are

Question 42

The truth table for an argument that has three component atomic statements will have six rows.

Question 43

The abbreviated truth table method can be used to prove that an argument is valid.

Question 44

If there is any assignment of truth values in which the premises are all , then the argument is invalid.

Question 45

A tautology is a statement that is necessarily false-that is, it is false regardless of the truth values assigned to the atomic statements that compose it.

Question 46

A statement that is false regardless of the truth values assigned to the atomic statements that compose it is a contradiction.

Question 47

Any argument with logically inconsistent premises will be valid yet unsound.

Question 48

A statement that is in at least one row is contingent.

Question 49

Two statements are logically equivalent when each validly implies the other.

Question 50

Two statements are logically equivalent when the biconditional connecting them is a tautology.

Question 51

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: A • C

Question 52

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: B • ~C

Question 53

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: D ⋁ B

Question 54

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: C → ~(C • B)

Question 55

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: A ↔ (C ⋁ D)

Question 56

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: B → ~(A • B)

Question 57

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))

Question 58

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: ~(A • B) ↔ (A → (C ⋁D))

Question 59

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: ~(A → C) • (C ⋁ ~D)

Question 60

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: ~(A ⋁ C) ↔ (B • ~(A ⋁ C))

Question 61

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: You can vote in the Democratic primary election only if you are a registered member of the Democratic Party. (V: You can vote in the Democratic primary election; R: You are a registered member of the Democratic Party.)

Question 62

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: It's not the
case that Sally is in love with James, though James is in love with Sally. (S: Sally is in love with James; J: James is in love with Sally.)

Question 63

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: The
presence of H₂O on Mars is sufficient for the production of life-forms. (H: H₂O is present on Mars; P: Life-forms are produced on Mars.)

Question 64

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Susan will
be able to go to the graduate school of her choice unless she scores very poorly on her GRE. (C: Susan is
able to go to the graduate school of her choice; P: Susan scores very poorly on her GRE.)

Question 65

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Unless
Sharon passes her final, she will get a C in the class. (P: Sharon passes her final; C: Sharon gets a C in the class.)

Question 66

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Although
Stephen scored high on the LSAT, he did not get into the law school of his choice. (S: Stephen scored
high on the LSAT; L: Stephen got into the law school of his choice.)

Question 67

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Both Al and
Bob failed to come to the party. (A: Al came to the party; B: Bob came to the party.)

Question 68

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Neither Jean
nor Ron is allergic to shellfish. (J: Jean is allergic to shellfish; R: Ron is allergic to shellfish.)

Question 69

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: It is not the
case that neither ostriches nor turkeys can fly. (O: Ostriches can fly; T: Turkeys can fly.)

Question 70

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Jones wins
only if Smith and Brown both lose. (J: Jones wins; S: Smith wins; B: Brown wins.)

Question 71

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Assuming
that Susie is at the horse show, Dee Dee is either at home or at work. (S: Susie is at the horse show; H:
Dee Dee is at home; W: Dee Dee is at work.)

Question 72

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: A necessary
condition for Adonis to go camping is that he behave and not bark at other dogs. (C: Adonis goes
camping; B: Adonis behaves; O: Adonis barks at other dogs.)

Question 73

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan's
attendance in class is both a necessary and sufficient condition for his passing this class. (A: Nathan
attends class; P: Nathan passes class.)

Question 74

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Both
Patricia and Scott are prepared for the test, but Henry is not. (P: Patricia is prepared for the test; S: Scott
is prepared for the test; H: Henry is prepared for the test.)

Question 75

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: Either
Abigail and Dieter both go to the dance or neither does. (A: Abigail goes to the dance; D: Dieter goes to the dance.)

Question 76

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: It will either
rain or snow, but not both. (R: It will rain; S: It will snow.)

Question 77

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: It will snow
if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B: It is
below 32° out; H: The humidity is greater than 60 percent.)

Question 78

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: If there's too much rain in the early spring and not enough during the summer, the tomato crop will not be very good. (S: There is too much rain in the spring; I: There is enough rain during the summer; G: The tomato crop is very good.)

Question 79

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: If the
argument has all conclusion, then the argument is not valid. (P: The argument
has all true premises; C: The argument has a true conclusion; V: The argument is valid.)

Question 80

Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan will go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term, finishes his English research paper, and does not lose his job. (C: Nathan will go to the Cayman Islands for spring break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English research paper; J: Nathan loses his job.)