Chapter 3 Review
Some A are not B can be expressed equivalently as
Not all A are B
Compound statement always true
Tautology
A truth table for p v ~ q requires four different truth tables
True
Compound statement consisting of two simple statements that are both false can be true
True
p <---> q = if p then q, and if q then p
True
Negation of a false statement
True statement
A conjunction, p ^ q is true only when...
both p and q are true.
The compound statement "If p, then q" is symbolized by ____ and is called a _____.
p ---> q, conditional
Negation of p ---> q
p ^ ~q ~(p ---> q)
To negate a disjunction, negate each of the component statements and change or to
And
A conditional statement is false only when the consequent is true and the antecedent is false.
False. The true statement is "A conditional statement is false only when the antecedent is true and the consequent is false."
p ^ q can be translated as "p but q."
True
A statement is a sentence either ___ but not both.
True or False
p ---> q = p is sufficient for q
True, because the biconditional statement p <--> q means p ---> q, is p is sufficient for q
p <---> q can be translated as "p is necessary and sufficient for q"
True, because the biconditional statement p <--> q means p --> q, so p is sufficient for q, and q --> p, so p is necessary for q.
The consequent is the necessary condition in a conditional statement.
True, because the conditional statement p ---> q means "q is necessary for p" and q is the consequent.
T/F A truth table for p V ~q requires four possible combinations of truth values.
True, because there are two possible values for p and q respectively.
T/F A truth table for (p v ~q) ^ r requires eight possible combinations of truth values.
True, because there are two possible values for p, q, and r respectively.
When symbolic statements are translated into English, the simple statements in parentheses appear on the same side of the comma.
True, because when statements are expressed in English commas are used to indicate groupings.
No A are B can be equivalently expressed as
All A are not B
To form the negation of a conditional statement, change the if-then connective to
And
Conditional statement is ___ to its contrapositive
Equivalent
Some implications are not tautologies
False
T/F Any argument with true premises is valid.
False
p ---> q = p is necessary for q
False
To negate a conjunction, negate each of the component statements and change and to
Or
Compound statement always false
Self-contradiction
Equivalent symbol
Three bar equal sign
An equivalent form for a conditional statement is obtained by reversing and negating the antecedent and consequent
True
T/F The conclusion of a sound argument is true relative to the premises, but it is also true as a separate statement removed from the premises.
True
The conclusion of a sound argument is true relative to the premises, but it is also true as a separate statement removed from the premises
True
p <---> q = p is necessary and sufficient for q
True
p <---> q can be translated as "If p then q, and if q then p."
True
If one component statement in a disjunction is true, the disjunction is true.
True.
Am argument is ____ if the conclusion is true whenever the premises are assumed to be true
Valid
A biconditional p <---> q is only true when
p and q have the same truth value
A conditional statement p ---> q is false when
p is true and q is false
Converse of p ---> q is
q ---> p
The converse of p ---> q is
q ---> p
Inverse of p ---> q
~ p ---> ~q
Contrapositive of p ---> q
~ q ---> ~ p
To form the negation of a conditional statement, leave the ___ and negate the ____
Antecedent, Consequent
Conditional statement is not equivalent to its
Converse or inverse
Compound statements that are made up of the same simple statements and have the same corresponding truth values for all true-false combos of these simple statements are said to be
Equivalent
A truth table for p v ~ p requires four different truth tables
False
Any argument with true premises is valid
False
Conditional statement is false when consequent is true and antecedent is false
False
Double negation of a statement is equivalent to the statements negation
False
If a conditional statement is true, it's inverse must be false
False
Negation of a true statement
False statement
Any argument whose premises are p ---> q and q ---> r is valid regardless of the conclusion
False, because if the argument has ~r as the conclusion, then the argument is not valid.
Using the dominance of connectives, p --> q ^ r means (p --> q) ^ r.
False, because the conditional connective is MORE DOMINANT than the conjunction connective. The statement p --> q ^ r means "if p, then q and r."
p v q = p or q but not both
False, because the connective V is an inclusive or, which means "either or both."
Conditional statement always true
Implications
Statements that include the words all, some, and no
Quantified statements
If one component statement in a conjunction is false, the conjunction is false.
The statement is TRUE because a conjunction is true only when both component statements are true.
Statement "all A are B" is expressed equivalently as
There are no A that are not B
Some A are B can be equivalently expressed as
There exists at least one A that is a B