Chapter 3: Logic Flashcards
A _______ is a sentence that is either true or false, but not both simultaneously.
Statement
As long as a sentence is either _____ or ______ that sentence is a statement
- true
- false
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
FALSE: It is still a statement even if you DON’T know whether or not it is true or false.
What are three different types of sentences that aren’t statements? Why are they not statements?
- opinions
- questions
- commands
- they aren’t statements because they aren’t true or false
_______ is the contradiction or denial of something.
Negation
The negation of a true statement is a _____ statement, while the negation of a false statement is a ______ statement.
- false
- true
In symbolic logic, we use lowercase letters such as ___, ___, ___, and ___ to represent statements
- p
- q
- r
- s
The negation of a statement p is written as ____
~p
Can letters such as p, q, or r represent any statement, including
English statements containing the word “not”?
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.
_______ _______ are statements containing the word(s) “all,” “some,” and/or “none.”
Quantified statement
The words “all,” “some,” and/or “none” are considered to be ________.
Quantifiers
It seems to me that the negation of “All writers are poets” should be “No writers are poets.” What’s
wrong with my thinking?
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.
A statement that conveys one idea without a connection of words is called a ____ _____.
simple statement
______ ______ are statements formed by combining two or more simple statements.
compound statements
Words that join simple statements to form a compound statement are called ________.
Connectives
What are five examples of connectives?
- and
- or
- if
- then
- if and only if
If p and q represent simple statements, then the compound statement of “p and q” is symbolized by:
p ^ q
The compound statement formed by connecting statements with the word “and” is called a ________. the symbol for the word “and” is:
- conjunction
TRUE or FALSE: If the word “and” is in a statement, it is automatically a conjunction
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.”)
The connective “or” can mean two different things. What are they?
- 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)
The compound statement formed by connecting with the word “or” is called ______. The symbol for “or” is:
- Disjunction
- V
The compound statement formed by connecting statements with “if-then” is called ______. The symbol for “if -then” is:
- conditional statement
- —> (arrow)
In a conditional statement, the symbol before the —> is called ______ and the symbol after the —> is called ______.
- antecedent
- consequent
The compound statement formed by connecting statements with “if and only if” is called _____. The symbol for “if and only if is:
- biconditional
- <—>
The statement “if and only if” can be abbreviated as ___.
iff
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.
- parentheses
- commas
- same side
If a symbolic statement appears without parentheses, statements before and after the most _______ _______ should be grouped.
dominant connective
When it comes to dominance of connectives, Symbolic connectives are categorized from the most dominant, the __________, to the least dominant, ________.
- biconditional
- negation
The dominance of connectives used in symbolic logic is defined in the following order:
- Biconditional
- conditional
- Conjunction, ^
Disjunction, V - Negation
Why is negation considered a connective?
because it does affect the truth value of a statement.
When are you supposed to use the dominance of connectives?
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.
A conjunction is only true when:
Both simple statements are true
When is a conjunction false?
As soon as you find one simple statement in a conjunction that is false, then the conjunction is false.
The statements making up a compound statement are called ________ ___________.
component statements
An “or” statement is true in every case, except when both component statements are ______.
false
When is a disjunction true?
As soon as you find one component statement in a disjunction that is true, then the disjunction is true.
A compound statement that is always true is called a __________.
tautology
When is a disjunction false?
When both component statements in the disjunction are false
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.
TRUE
Conditional statements that are tautologies are called ________.
implications
Some compound statements are false in all possible cases. Such statements are called __________________.
self-contradictions.
The only case in which a conditional is false is when:
the first component statement, the antecedent, is true and the second component statement, the consequent, is false.
A biconditional is true only when:
the component statements have the same truth value.
_________ ____________ ___________ are made up of the same simple statements and have the same corresponding truth values for all true–false combinations of these simple statements.
Equivalent compound statements
Which special symbol is used to show that two statements are equivalent?
≡
~(~p) ≡ p illustrates that the ________ ________
of a statement is _________ to the statement.
- double negation
- equivalent
The __________ of a conditional statement is a statement obtained by reversing and negating the antecedent and the consequent.
contrapositive
If a compound statement is true, then its equivalent statement:
must also be true
If a compound statement is false, then its equivalent statement:
must also be false
Truth tables are used to show that two statements are _________.
equivalent.
The truth value of a conditional statement does not change if the antecedent and consequent are __________ and both are _________.
- reversed
- negated
