Question 1

Which is not one of the nine rules of inference?&#10;A)simplification&#10;B)modus tollens&#10;C)subtraction&#10;D)absorption

Accepted Answer

Subtraction is not one of the nine rules of inference used in logic and argumentation. The nine rules typically include simplification, modus tollens, and absorption among others, but subtraction is not recognized as a formal rule of inference in logical arguments.

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

constructive dilemma

Accepted Answer

This formula represents the constructive dilemma rule of inference. It states that if we know $p$ implies $q$ and $r$ implies $s$, and either $p$ or $r$ is true, then either $q$ or $s$ must be true.

Question 3

What is the formula for simplification?&#10;A)p &#183; q ? p&#10;B)p q ? p &#183; q&#10;C)p ? $p\vee q$&#10;D)p &#183; q, p, ?q

Accepted Answer

p &#183; q ? p&#10;

Question 4

&#34;Either I get married or I live alone; I didn't get married; therefore, I live by myself.&#34; What is the elementary valid argument form of this argument?&#10;A)constructive dilemma&#10;B)modus tollens&#10;C)disjunctive syllogism&#10;D)hypothetical syllogism

Accepted Answer

This argument is an example of a disjunctive syllogism, which has the form: Either A or B; not A; therefore, B. In this case, A is "I get married" and B is "I live alone." The argument states that one of these must be true, A is not true, therefore B must be true.

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

Accepted Answer

The rule of inference used here is double negation, which allows the removal or introduction of double negatives. In this case, "~~A" is equivalent to "A", making the statements logically equivalent.

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

Accepted Answer

The argument uses disjunctive syllogism, which allows one to infer one disjunct when the other is shown to be false. Here, since $ [F ? (G ? ~H)] $ is negated and the whole expression is true, $ I \vee J $ must be true.

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

Accepted Answer

The answer of By which rule of inference does the...

Question 8

The method of proving invalidity by assigning truth values to statements in a shortened truth table:&#10;A)can become more cumbersome than the full truth table method because of the time and energy involved&#10;B)works only with modus tollens and modus ponens&#10;C)is resorted to for convenience-it saves time and space&#10;D)is not as accurate as using Venn diagrams

Accepted Answer

The shortened truth table method is used for convenience because it saves time and space by focusing only on the necessary parts of the table to prove invalidity, rather than constructing a full truth table.

Question 9

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

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k this deck

Accepted Answer

The rule of inference used here is tautology, which involves repeating the same statement or formula. In this case, $[F ? ~(G \vee H)] ? (I \vee J)$ is repeated, making the argument a tautology.

Question 10

Which rule of inference makes the conclusion of this argument follow from its premise?&#10;A ? B&#10; ? (~A ? ~B)&#10;A)addition&#10;B)exportation&#10;C)commutation&#10;D)transposition

Accepted Answer

Transposition is the rule of inference that allows one to infer the conclusion (~A → ~B) from the premise (A → B). It involves flipping the antecedent with the consequent and negating both.

Question 11

Conjunction is symbolically represented by p, q, ? p &#183; q.

Accepted Answer

The answer of Conjunction is symbolically represented by p, q,...

Question 12

Simplification is symbolically represented by p ? q, ? (p &#183; q).

Accepted Answer

The answer of Simplification is symbolically represented by p ?...

Question 13

You can replace [(p &#183; q) ?r] with [p ?(q ?r)].

Accepted Answer

The answer of You can replace [(p &#183; q) ?r]...

Question 14

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

Accepted Answer

The answer of One of De Morgan's theorems states that\(...

Question 15

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

Accepted Answer

The answer of Material implication states that$ (~p\vee q)$ is...

Question 16

Matching:&#10;&#10;-An argument is proved invalid when its premises are ________ and its conclusion is false in one line of its truth table.&#10;A)false&#10;B)true&#10;C)ambiguous

Accepted Answer

The answer of Matching:&#10;&#10;-An argument is proved invalid when its...

Question 17

Matching:&#10;&#10;-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 ________.&#10;A)valid&#10;B)invalid&#10;C)unsound

Accepted Answer

The answer of Matching:&#10;&#10;-If no truth values can be given...

Question 18

Matching:&#10;&#10;-When the rule of ________ is applied to &#34;If it rains, I will get wet,&#34; it becomes &#34;If it rains, not only will it be raining but I will get wet.&#34;&#10;A)addition&#10;B)absorption&#10;C)simplification

Accepted Answer

The answer of Matching:&#10;&#10;-When the rule of ________ is applied...

Question 19

Matching:&#10;&#10;-&#34;p &#183; q, ? p&#34; is the form of ________.&#10;A)simplification&#10;B)disjunction&#10;C)addition

Accepted Answer

The answer of Matching:&#10;&#10;-&#34;p &#183; q, ? p&#34; is the...

Question 20

Matching:&#10;&#10;-We can use ________ to substitute (p ? q) for (~pV q)&#10;A)material implication&#10;B)De Morgan's rule&#10;C)simplification

Accepted Answer

The answer of Matching:&#10;&#10;-We can use ________ to substitute (p...

Deck 9: Propositional Logic II