Deck 9: Propositional Logic-Propositions

Question 1

In the statement form p • q, the component statement variables p and q are called:

A)conjuncts
B)disjuncts
C)antecedents
D)consequents
E)There is no special name for the component statements.

Answer 1

A

Question 2

The connective "•" is called:

A)"dot"
B)"tilde"
C)"wedge"
D)"horseshoe"
E)"triple bar"

Answer 2

A

Question 3

The connective "~" is called:

A)"dot"
B)"tilde"
C)"wedge"
D)"horseshoe"
E)"triple bar"

Answer 3

B

Question 4

The connective used for conjunctions is:

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 5

The connective used for negations is:

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 6

In the truth table for the statement form ~p, the column of truth values underneath the main connective should be:

A)TF
B)FT
C)TFTF
D)TTFF
E)FFTT

Question 7

The statement form p $\bigwedge$ q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 8

In the truth table for the statement form p $\bigvee$ q, the column of truth values underneath the main connective should be:

A)TTTF
B)TFFF
C)TFTT
D)TTFF
E)TFFT

Question 9

Symbolize "not both p and q."

A)~p • ~q
B)~p • q
C)~( p • q)
D)( p vq) • ~( p • q)
E)( pv q) • (~p q)

Question 10

The statement form ¬ p is:

A)a negation
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 11

The connective used for biconditionals is:

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 12

The statement form p & q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 13

The connective used for disjunctions is:

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 14

Choose which symbol to use for "it is not the case that," "it is false that," and "n't."

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 15

The statement form ~p is:

A)a conjunction
B)a negation
C)a disjunction
D)a conditional
E)not actually a statement form

Question 16

Symbolize "both not p and not q."

A)~p • ~q
B)~p • q
C)~( p • q)
D)( p v q) • ~( p • q)
E)( p v q) • (~p q)

Question 17

Choose which symbol to use for "but," "however," "nevertheless," and "although."

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 18

The statement form p • q is:

A)a conjunction
B)a negation
C)a disjunction
D)a conditional
E)not actually a statement form

Question 19

In the truth table for the statement form p • q, the column of truth values underneath the main connective should be:

A)TTTF
B)TFFF
C)TFTT
D)TTFF
E)TFFT

Question 20

The connective used for conditionals is:

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 21

The connective " $\equiv$ " is called:

A)"dot"
B)"tilde"
C)"wedge"
D)"horseshoe"
E)"triple bar"

Question 22

The statement form p $\equiv$ q is:

A)a conjunction
B)a negation
C)a disjunction
D)a biconditional
E)not actually a statement form

Question 23

The connective " $\bigvee$ " is called:

A)"dot"
B)"tilde"
C)"wedge"
D)"horseshoe"
E)"triple bar"

Question 24

The connective " $\supset$ " is called:

A)"dot"
B)"tilde"
C)"wedge"
D)"horseshoe"
E)"triple bar"

Question 25

Choose which symbol to use for "provided," "given that," "supposing that," "unless," and "only if."

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 26

Choose which symbol to use for "just in case" and "just in the event that."

A)•
B)~
C) $\bigvee$
D) $\supset$
E) $\equiv$

Question 27

The statement form p $\supset$ q is:

A)a conjunction
B)a negation
C)a disjunction
D)a conditional
E)not actually a statement form

Question 28

The statement form p $\rightarrow$ q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 29

In the statement form p $\equiv$ q, the component statement variables p and q are called:

A)conjuncts
B)disjuncts
C)antecedents
D)consequents
E)There is no special name for the component statements.

Question 30

The statement form p $\equiv$ q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 31

In the statement form p $\bigvee$ q, the component statement variables p and q are called:

A)conjuncts
B)disjuncts
C)antecedents
D)consequents
E)There is no special name for the component statements.

Question 32

The statement form p $\bigvee$ q is:

A)a conjunction
B)a negation
C)a disjunction
D)a conditional
E)not actually a statement form

Question 33

In the truth table for the statement form p $\equiv$ q, the column of truth values underneath the main connective should be:

A)TTTF
B)TFFF
C)TFTT
D)TTFF
E)TFFT

Question 34

The statement form p $\subset$ q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 35

Symbolize "neither p nor q."

A)~p $\bigvee$ ~q
B)(~p $\bigvee$ ~q) • (p • q)
C)~( p $\bigvee$ q)
D)( p $\bigvee$ q) • ~( p • q)
E)( p $\bigvee$ q) • (~p $\supset$ q)

Question 36

In the statement form p $\supset$ q, the component statement variable p is called:

A)the conjunct
B)the disjunct
C)the antecedent
D)the consequent
E)There are no special names for the component statements.

Question 37

In the truth table for the statement form p $\supset$ q, the column of truth values underneath the consequent should be:

A)TF
B)TTFF
C)TFTF
D)TTTTFFFF
E)TTFFTTFF

Question 38

Symbolize "p or q but not both."

A)p $\bigvee$ q
B)(p $\bigvee$ q) • (~p • ~q)
C)(p $\bigvee$ q) • ~(p $\supset$ q)
D)(p $\bigvee$ q) • ~(p • q)
E)(p $\bigvee$ q) • (~p $\supset$ q)

Question 39

In the truth table for the statement form p $\supset$ q, the column of truth values underneath the main connective should be:

A)TTTF
B)TFFF
C)TFTT
D)TTFF
E)TFFT

Question 40

In the truth table for the statement form p $\supset$ q, the column of truth values underneath the antecedent should be:

A)TF
B)TTFF
C)TFTF
D)TTTTFFFF
E)TTFFTTFF

Question 41

The statement form p $\leftrightarrow$ q is:

A)a conjunction
B)a disjunction
C)a conditional
D)a biconditional
E)not actually a statement form

Question 42

Identify which of the following is a correct symbolization of the following statement. The doctors X-rayed my head and did not find anything.

A)X • ~F
B)X $\bigvee$ ~F
C)X $\supset$ ~F
D)X $\equiv$ ~F
E)X $\supset$ F

Question 43

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.

A)~S • ~I
B)~S $\bigvee$ ~I
C)~S $\supset$ ~I
D)~S $\equiv$ ~I
E)S $\supset$ ~I

Question 44

If both conjuncts of a conjunction are tautologies, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 45

Identify the main connective in the following statement. {[(P $\supset$ P) $\supset$ P] $\supset$ P} $\supset$ (P $\supset$ P)

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 46

In the truth table for the statement form ( p • q) $\supset$ p, the column of truth values underneath the main connective should be TTTT.Therefore, this statement form is a:

A)tautology
B)self-contradiction
C)contingency
D)equivalency
E)contradiction

Question 47

Identify the main connective in the following statement. [(G • O) $\bigvee$ (A $\supset$ ~M)] $\equiv$ [(G • O) $\bigvee$ (A $\supset$ ~M)]

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 48

Identify the main connective in the following statement. (D • N) $\bigvee$ G

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 49

Identify which of the following is a correct symbolization of the following statement. If you argue with a fool, people might not know who is the fool.

A)A • ~K
B)A $\bigvee$ ~K
C)A $\supset$ ~K
D)A $\equiv$ ~K
E)~A $\supset$ K

Question 50

Identify which of the following is a correct symbolization of the following statement. The Greeks won the battle but lost the war.

A)B • W
B)B $\bigvee$ W
C)B $\supset$ W
D)B $\equiv$ W
E)B $\supset$ ~W

Question 51

Identify the main connective in the following statement. {[(F $\bigvee$ R) $\equiv$ ~(W • T)] • (N • P)} $\bigvee$ (L $\supset$ ~M)

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 52

Identify the main connective in the following statement. (N $\equiv$ T) $\supset$ [(S $\bigvee$ M) • ~(H $\bigvee$ T)]

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 53

Identify the main connective in the following statement. L $\supset$ [(W $\supset$ L) $\bigvee$ ~(Y $\supset$ T)]

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 54

Identify the main connective in the following statement. [(N • D) $\bigvee$ (T $\equiv$ M)] $\supset$ ~N

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 55

The negation of a self-contradiction is itself a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 56

Identify the main connective in the following statement. (D $\supset$ N) • (F $\supset$ Y)

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 57

Identify the main connective in the following statement. [(F $\equiv$ L) $\equiv$ (L $\supset$ I)] • (S $\bigvee$ T)

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 58

Identify which of the following is a correct symbolization of the following statement. If the shoe fits, then one has to wear it.

A)F • W
B)F $\bigvee$ W
C)F $\supset$ W
D)F $\equiv$ W
E)F

Question 59

Identify the main connective in the following statement. (T $\bigvee$ ~E) $\equiv$ (C • M)

A)•
B) $\bigvee$
C) $\supset$
D) $\equiv$
E)~

Question 60

Below is an incomplete truth table for the statement form [( p $\supset$ q) • p] $\supset$ q. $$\begin{array} { c | c | c | c | c | c | c } { [ ( p } & \supset & q ) & \bullet & p ] & \supset & q \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } & & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T } & & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } & & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } & & \mathrm { F }\end{array}$$ The truth-value assignment underneath the main connective should be TTTT.Therefore, the statement form [( p $\supset$ q) • p] $\supset$ q is a:

A)tautology
B)self-contradiction
C)contingency
D)equivalency
E)contradiction

Question 61

If neither disjunct of a disjunction is a tautology, then the disjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 62

The negation of a tautology is itself a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 63

If both main components of a biconditional are tautologies, then the biconditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 64

If the antecedent of a conditional is a tautology, then the conditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 65

If at least one disjunct of a disjunction is a tautology, then the disjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 66

If the antecedent of a conditional is a self-contradiction, then the conditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 67

If at least one conjunct of a conjunction is a tautology, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 68

If only one conjunct of a conjunction is a tautology, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 69

If both conjuncts of a conjunction are self-contradictions, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 70

If only one conjunct of a conjunction is a self-contradiction, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 71

If both main components of a biconditional are self-contradictions, then the biconditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 72

If neither main component of a biconditional is a tautology, then the biconditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 73

If only one main component of a biconditional is a tautology, then the biconditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 74

In the truth table for the statement form ~(p $\supset$ p), the column of truth values underneath the main connective should be FF.Therefore, this statement form is a:

A)tautology
B)self-contradiction
C)contingency
D)equivalency
E)contradiction

Question 75

If the consequent of a conditional is a tautology, then the conditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 76

If only one disjunct of a disjunction is a tautology, then the disjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 77

If at least one conjunct of a conjunction is a self-contradiction, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 78

If both disjuncts of a disjunction are tautologies, then the disjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 79

If at least one main component of a biconditional is a tautology, then the biconditional itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given

Question 80

If neither conjunct of a conjunction is a tautology, then the conjunction itself is a:

A)tautology
B)self-contradiction
C)contingency
D)coherency
E)unable to determine from the information given