Chapter 8

Question 1

________ proposition combines two or more component propositions by means of a connective.

Answer 1

Compound propositions

Question 2

Compound propositions that use the connective “or” are called ______ propositions.

Answer 2

disjunctive propositions

Question 3

Compound propositions that use the connective if . .. then are called ______ propositions.

Answer 3

hypothetical

Question 4

Categorical syllogism is a form of deductive reasoning and there are two types of non-categorical syllogisms that have:

Answer 4

Disjunctive and hypothetical propositions as premises

Question 5

Name types of connectives that are used in compound propositions

Answer 5

“or” and “if….then”

Question 6

The compound proposition that contains “or” is what type of proposition

Answer 6

disjunctive

Question 7

The compound proposition that contains “if…. then” is what kind of proposition

Answer 7

hypothetical

Question 8

Hypothetical propositions have the form “______” and they serve as premises in several types of inference.

Answer 8

If p, then q

Question 9

An inference that uses “or” is the form of what kind of

syllogism?

Answer 9

Disjunctive

Question 10

An antecedent in a hypothetical proposition is represented by which part of the “If p, then q” form?

Answer 10

“If X “ = antecedent

Question 11

An consequent in a hypothetical proposition is represented by which part of the “If p, then q” form?

Answer 11

“then X “ = consequent

Question 12

In the following hypothetical proposition which is the antecedent?

If it rains, then the graduation will be held in the gym

Answer 12

If it rains

Question 13

In the following hypothetical proposition which is the consequent?

If it rains, then the graduation will be held in the gym

Answer 13

then the graduation will be held in the gym

Question 14

In a ______ proposition, we are not actually asserting the truth of the antecedent or the consequent. We are saying that the truth of the first would be sufficient to guarantee the truth of the second. Until we know that it actually is raining, the possibility that the graduation will be held in the gym is merely ______. It is not something we can assert categorically.

Answer 14

hypothetical | hypothetical

Question 15

Hypothetical propositions are used pervasively in ordinary speech to identify relationships of …..

Answer 15

dependence among facts , events, or possibilities.

Question 16

______ are used pervasively in ordinary speech to identify relationships of dependence among facts , events, or possibilities.

Answer 16

Hypothetical propositions

Question 17

Consider the statements:

2. If I were president of the United States, I would be a politician.
3. If I were a politician, I would be president of the United States.

These statements are examples of _____ propositions in which “if p, then q” is NOT equivalent to “if q, then p”

Answer 17

Hypothetical propositions

These are clearly not equivalent; 2 is true by definition (anyone who holds elective office must be a politician) , whereas 3 is dubious to say the least.

Question 18

Hypothetical propositions are similar to that of “A” (universal, affirm) _______ propositions because the premise is not equivalent when the predicate and subject order is inverted.

Answer 18

categorical propositions

Question 19

Another point of similarity between “A” categorical propositions and hypothetical propositions is that both have a valid ______. “All S are P” is equivalent to “All
non-P are non-S.” In the same way, “if p, then q” is equivalent to “if not-q, then not -p.”

For example:
4. If it rained last night , then the ground is wet this morning.

5. If the ground is not wet this morning, then it did not rain last night.

These propositions are clearly equivalent, and it ‘s easy to see why the equivalence holds as a general rule.

Answer 19

contrapositive

Question 20

The standard form of ________ propositions
is

If [antecedent], then [ consequent].

Answer 20

hypothetical

Question 21

The antecedent and consequent are component

propositions that we represent by

Answer 21

lowercase letters : p, q, r, … not-p, not-q , not-r , …

Question 22

The following are examples of what kind of form in a hypothetical statement/proposition:

p if q
p only if q
p if and only if q
p unless q
without X, q

Answer 22

Non-standard form

Question 23

The following are examples of what kind of form in a hypothetical statement/proposition:

If q, then p
If p, then q
If q, then p and if p then q
if not q, then p
If X does not exist (occur), then q

Answer 23

Standard form

Question 24

Syllogisms are

Answer 24

are types of arguments with two premises and a conclusion (so, three statements total)

Question 25

There are three major types of syllogism:

Answer 25

categorical, disjunctive, and hypothetical syllogisms

Question 26

If any argument (including any syllogism) is valid, then, when the argument’s premises are true, its conclusion must be _____.

Answer 26

true

Question 27

________ syllogisms are useful in scientific reasoning, e.g., “either the cause of the sickness is factor A or factor B. It’s not A, so it is B.” When we rule out alternative explanation, we are reasoning by _______ syllogism.

Answer 27

Disjunctive