Deck 9: Propositional Logic II

Question 1

Which is not one of the nine rules of inference?

A)simplification
B)modus tollens
C)subtraction
D)absorption

Answer 1

subtraction

Question 2

Which of the rules of inference is described by this formula?
(p ? q) · (r ? s)
$p\vee r$
? $q\vee s$

A)conjunction
B)absorption
C)disjunctive syllogism
D)constructive dilemma

Answer 2

constructive dilemma

Question 3

What is the formula for simplification?

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

Answer 3

p · q ? p

Question 4

"Either I get married or I live alone; I didn't get married; therefore, I live by myself." What is the elementary valid argument form of this argument?

A)constructive dilemma
B)modus tollens
C)disjunctive syllogism
D)hypothetical syllogism

Question 5

What is the rule of inference by which the conclusion of this argument follows from the premise?
C ? (A ? B)
? C ? (~~A ? B)

A)distribution
B)double negation
C)addition
D)constructive dilemma

Question 6

For the following valid argument, state the rule of inference by which the conclusion follows from its premises:
$[F ? (G ? ~H)] \vee(I \vee J) ~[F ? (G ? ~H)]$ ? $I \vee J$

A)constructive dilemma
B)disjunctive syllogism
C)absorption
D)modus ponens

Question 7

By which rule of inference does the conclusion of this argument follow from its premises?
$~(A · B)$ ? $(C \vee D)$ ~ $(A · B)$ ? $(C \vee D)$

A)modus ponens
B)modus tollens
C)disjunctive syllogism
D)simplification

Question 8

The method of proving invalidity by assigning truth values to statements in a shortened truth table:

A)can become more cumbersome than the full truth table method because of the time and energy involved
B)works only with modus tollens and modus ponens
C)is resorted to for convenience-it saves time and space
D)is not as accurate as using Venn diagrams

Question 9

Which rule of inference makes the conclusion of this argument follow from its premise?
$[F ? ~(G \vee H)] ? (I \vee J) ?{[F ? ~(G\vee H)] · [F ? ~(G \vee H)]} ? (I \vee J)$

A)transportation
B)tautology
C)association
D)commutation

Question 10

Which rule of inference makes the conclusion of this argument follow from its premise?
A ? B
? (~A ? ~B)

A)addition
B)exportation
C)commutation
D)transposition

Question 11

Conjunction is symbolically represented by p, q, ? p · q.

Question 12

Simplification is symbolically represented by p ? q, ? (p · q).

Question 13

You can replace [(p · q) ?r] with [p ?(q ?r)].

Question 14

One of De Morgan's theorems states that $(p\vee q)$ is logically equivalent to $(q\vee p)$ .

Question 15

Material implication states that $(~p\vee q)$ is logically equivalent to (p ?q).

Question 16

Matching:

-An argument is proved invalid when its premises are ________ and its conclusion is false in one line of its truth table.

A)false
B)true
C)ambiguous

Question 17

Matching:

-If no truth values can be given to the statements of an argument to make its premises true and its conclusion false, then the argument must be ________.

A)valid
B)invalid
C)unsound

Question 18

Matching:

-When the rule of ________ is applied to "If it rains, I will get wet," it becomes "If it rains, not only will it be raining but I will get wet."

A)addition
B)absorption
C)simplification

Question 19

Matching:

-"p · q, ? p" is the form of ________.

A)simplification
B)disjunction
C)addition

Question 20

Matching:

-We can use ________ to substitute (p ? q) for (~pV q)

A)material implication
B)De Morgan's rule
C)simplification