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)

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

To negate a disjunction, negate each of the component statements and change or 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

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.

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."

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."

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