Chapter 3: Logic

Question 1

A _______ is a sentence that is either true or false, but not both simultaneously.

Answer 1

Statement

Question 2

As long as a sentence is either _____ or ______ that sentence is a statement

Answer 2

• true
• false

Question 3

TRUE or FALSE: In order for a sentence to be considered a statement, you need to know whether or not it is true or false

Answer 3

FALSE: It is still a statement even if you DON’T know whether or not it is true or false.

Question 4

What are three different types of sentences that aren’t statements? Why are they not statements?

Answer 4

• opinions
• questions
• commands
• they aren’t statements because they aren’t true or false

Question 5

_______ is the contradiction or denial of something.

Answer 5

Negation

Question 6

The negation of a true statement is a _____ statement, while the negation of a false statement is a ______ statement.

Answer 6

• false
• true

Question 7

In symbolic logic, we use lowercase letters such as ___, ___, ___, and ___ to represent statements

Answer 7

• p
• q
• r
• s

Question 8

The negation of a statement p is written as ____

Answer 8

~p

Question 9

Can letters such as p, q, or r represent any statement, including
English statements containing the word “not”?

Answer 9

Yes. When choosing letters to represent statements, you may prefer to use the symbol ∼ with negated English statements.
However, it is not wrong to let p, q, or r represent such statements.

Question 10

_______ _______ are statements containing the word(s) “all,” “some,” and/or “none.”

Answer 10

Quantified statement

Question 11

The words “all,” “some,” and/or “none” are considered to be ________.

Answer 11

Quantifiers

Question 12

It seems to me that the negation of “All writers are poets” should be “No writers are poets.” What’s
wrong with my thinking?

Answer 12

The negation of “All writers are poets” cannot be “No writers are poets” because both statements are false. The negation of a false statement must be a true statement. In general, the negation of “All A are B” is not “No A are B.

Question 13

A statement that conveys one idea without a connection of words is called a ____ _____.

Answer 13

simple statement

Question 14

______ ______ are statements formed by combining two or more simple statements.

Answer 14

compound statements

Question 15

Words that join simple statements to form a compound statement are called ________.

Answer 15

Connectives

Question 16

What are five examples of connectives?

Answer 16

1. and
2. or
3. if
4. then
5. if and only if

Question 17

If p and q represent simple statements, then the compound statement of “p and q” is symbolized by:

Answer 17

p ^ q

Question 18

The compound statement formed by connecting statements with the word “and” is called a ________. the symbol for the word “and” is:

Answer 18

• conjunction

Question 19

TRUE or FALSE: If the word “and” is in a statement, it is automatically a conjunction

Answer 19

FALSE: If the statement cannot be broken down into two simple statements, it is itself a simple statement (e.g. “nonviolence and truth are inseparable.”)

Question 20

The connective “or” can mean two different things. What are they?

Answer 20

• exclusive or, which means “one or the other, but not both (ie. I visited London or Paris.)
• inclusive or, which means “either or both” (ie. I visited London or Paris or both)

Question 21

The compound statement formed by connecting with the word “or” is called ______. The symbol for “or” is:

Answer 21

• Disjunction
• V

Question 22

The compound statement formed by connecting statements with “if-then” is called ______. The symbol for “if -then” is:

Answer 22

• conditional statement
• —> (arrow)

Question 23

In a conditional statement, the symbol before the —> is called ______ and the symbol after the —> is called ______.

Answer 23

• antecedent
• consequent

Question 24

The compound statement formed by connecting statements with “if and only if” is called _____. The symbol for “if and only if is:

Answer 24

• biconditional
• <—>

Question 25

The statement "if and only if" can be abbreviated as ___.

Answer 25

iff

Question 26

Many compound statements contain more than one connective. When expressed symbolically, _________ are used to indicate which simple statements are grouped together. When expressed in English, _________ are used to indicate the groupings. When we translate the symbolic statement into English, the simple statements in parentheses appear on the ______ _______ of the comma.

Answer 26

- parentheses - commas - same side

Question 27

If a symbolic statement appears without parentheses, statements before and after the most _______ _______ should be grouped.

Answer 27

dominant connective

Question 28

When it comes to dominance of connectives, Symbolic connectives are categorized from the most dominant, the __________, to the least dominant, ________.

Answer 28

- biconditional - negation

Question 29

The dominance of connectives used in symbolic logic is defined in the following order:

Answer 29

1. Biconditional 2. conditional 3. Conjunction, ^ Disjunction, V 4. Negation

Question 30

Why is negation considered a connective?

Answer 30

because it does affect the truth value of a statement.

Question 31

When are you supposed to use the dominance of connectives?

Answer 31

Only apply the dominance of connectives if grouping symbols (parentheses) are not given in compound symbolic statements or commas do not appear in compound English statements.

Question 32

A conjunction is only true when:

Answer 32

Both simple statements are true

Question 33

When is a conjunction false?

Answer 33

As soon as you find one simple statement in a conjunction that is false, then the conjunction is false.

Question 34

The statements making up a compound statement are called ________ ___________.

Answer 34

component statements

Question 35

An "or" statement is true in every case, except when both component statements are ______.

Answer 35

false

Question 36

When is a disjunction true?

Answer 36

As soon as you find one component statement in a disjunction that is true, then the disjunction is true.

Question 37

A compound statement that is always true is called a __________.

Answer 37

tautology

Question 38

When is a disjunction false?

Answer 38

When both component statements in the disjunction are false

Question 39

TRUE or FALSE: Every time you hear or utter a conditional statement, you can reverse and negate the antecedent and consequent, and the statement’s truth value will not change.

Answer 39

TRUE

Question 40

Conditional statements that are tautologies are called ________.

Answer 40

implications

Question 41

Some compound statements are false in all possible cases. Such statements are called __________________.

Answer 41

self-contradictions.

Question 42

The only case in which a conditional is false is when:

Answer 42

the first component statement, the antecedent, is true and the second component statement, the consequent, is false.

Question 43

A biconditional is true only when:

Answer 43

the component statements have the same truth value.

Question 44

_________ ____________ ___________ are made up of the same simple statements and have the same corresponding truth values for all true–false combinations of these simple statements.

Answer 44

Equivalent compound statements

Question 45

Which special symbol is used to show that two statements are equivalent?

Answer 45

≡

Question 46

~(~p) ≡ p illustrates that the ________ ________ of a statement is _________ to the statement.

Answer 46

- double negation - equivalent

Question 47

The __________ of a conditional statement is a statement obtained by reversing and negating the antecedent and the consequent.

Answer 47

contrapositive

Question 48

If a compound statement is true, then its equivalent statement:

Answer 48

must also be true

Question 49

If a compound statement is false, then its equivalent statement:

Answer 49

must also be false

Question 50

Truth tables are used to show that two statements are _________.

Answer 50

equivalent.

Question 51

The truth value of a conditional statement does not change if the antecedent and consequent are __________ and both are _________.

Answer 51

- reversed - negated