Deck 8: Propositional Logic I

Question 1

How could you symbolize the statement, "I will love you unless you kiss me"?

A) $L \vee K$
B)L ? K
C) $~L\vee K$
D)L ? K

Answer 1

$L \vee K$

Question 2

~(p · ~q) is the same as:

A)~p · q
B)~p · ~q
C)(~p · ~q)
D)p ? q

Answer 2

p ? q

Question 3

What is the symbolic representation of modus tollens?

A)p ? q q ? p
B)p ? q p ? q
C)p ? q ~q ? ~p
D)p ? q, ~q, ? p

Answer 3

p ? q ~q ? ~p

Question 4

q and ~~q mean the same thing.What does this illustrate?

A)material equivalence
B)logical equivalence
C)repetition
D)double negation

Question 5

"I will either kill you, or I will love you." This statement might be symbolized as:

A) $K\vee L$
B)~K · L
C)~K ? L
D)K ? L

Question 6

"p ? q is logically equivalent to $~p\vee q$ ." This statement is:

A)De Morgan's Theorem
B)the definition of material implication
C)a negation of the conjunction of two statements
D)an invalid argument

Question 7

Let B symbolize the statement "All birds are beautiful." Then ~B must symbolize all of the following, except:

A)Some bird is not beautiful.
B)No birds are beautiful.
C)It is not the case that all birds are beautiful.
D)It is false that all birds are beautiful.

Question 8

"If you can't use a computer, you won't get a job.I can use a computer very well, so I'm going to get a good job!"
What is the best symbolic representation of this argument?

A)p ? q ~p ? ~q
B) $~p\vee ~q$ p ? ~q
C)p ? q ~q ? ~p
D)~p ? ~q, p, ? ~q

Question 9

"If dogs can fly, then the Earth is a sponge." Is this statement true?
Why or why not?

A)This is a contingent statement since it may be either true or false.
B)This is false but we must check the world to discover this.
C)This is false as neither the consequent nor the antecedent is true.
D)This is a true statement because it is in the form of a material conditional and has a false antecedent.

Question 10

Let B mean "the bread rises" and Y abbreviate "the yeast is good." The he compound statement B ? Y correctly represents any of the following propositions, except:

A)That the yeast is good is a necessary condition for the bread to rise.
B)That the yeast is good is a sufficient condition for the bread to rise.
C)The bread rises only if the yeast is good.
D)If the bread rises, the yeast is good.

Question 11

The following two arguments share the same argument form: "If wishes were horses, beggars could ride; beggars cannot ride; so wishes are not horses." "If price fixing becomes a common practice, the consumer will lose choices and taxpayers will be burdened with debt.We do not want consumers to lose choices and be burdened with debt, so we know that we should not allow price fixing."

Question 12

A truth table for an argument contains one row in which there are Ts under the
premises and an F under the conclusion.This single row shows that the entire argu-
ment is invalid.

Question 13

Another term for material equivalence is material implication.

Question 14

If an argument form is expressed as a conditional (with the conclusion as the consequent and a conjunction of the premises as the antecedent), and it shows one row on its truth table where Ts appear under the premises but an F appears under the conclusion, it may still be valid

Question 15

The principle of excluded middle asserts that no statement can be both true and
false at the same time.

Question 16

Matching:

-Two statements are logically equivalent if their biconditional is a ________.

A)tautology
B)statement
C)Proposition

Question 17

Matching:

-p ? q is ________ equivalent to ~pV q.

A)sufficiently
B)logically
C)empirically

Question 18

The only way for a disjunction to be false is if both of the disjuncts are proven to be ________ simultaneously.

A)True
B)False
C)Invalid

Question 19

Matching:

-Any statement is a ________ instance of its own statement form.

A)substitution
B)logical
C)Sufficient

Question 20

Matching:

-A conjunction is true only when both of its conjuncts are ________

A)false
B)true
C)valid