Test Bank for Discrete Mathematics and Its Applications, 8th
Edition by Rosen, 9781259676512, Covering Chapters 1-13 |
Includes Rationales
connectives - ANSWER: logical operators used to form new propositions from two or more existing
propositions
conjunction - ANSWER: "and"; true only when both propositions are true
disjunction - ANSWER: "or"; false only when both propositions are false
exclusive or - ANSWER: true only when exactly one of the propositions is true and false otherwise
implication - ANSWER: conditional statement; "if p, then q" false when p is true and q is false, true
otherwise.
converse of p->q - ANSWER: q->p; equivalent to inverse
contrapositive p->q - ANSWER: not q -> not p; has the same truth value as p->q always
inverse of p->q - ANSWER: not p -> not q; equivalent to converse
equivalent - ANSWER: two compound propositions always having the same truth value
biconditionals (bi-implications; biconditional statements) - ANSWER: if and only if; true only when p
and q have the same truth values; iff
Precedence of logical operators - ANSWER: negation, conjunction, disjunction, conditional,
biconditional
bit - ANSWER: symbol with two possible values, namely 0 and 1
boolean variable - ANSWER: a variable with a value of either true or false
bit string - ANSWER: sequence of zero or more bits; the length of this string is the number of bits in
the string
tautology - ANSWER: a compound proposition that is always true, no matter what the truth values of
the propositional variables that occur in it (emphasis on always)
contradiction - ANSWER: a compound proposition that is always false
contingency - ANSWER: a compound proposition that is always true
logically equivalent - ANSWER: compound propositions that have the same truth values in all possible
cases; when these two propositions, p and q, in the compound proposition p iff q is a tautology.
(emphasis on truth values)
distributive law (disjunction over conjunction) - ANSWER: p V (q^r) = (p v q) ^ (p v r)
De Morgan's Laws - ANSWER: how to negate conjunctions and disjunctions; the negation of a
disjunction is the conjunction of the negation of the components; the negation of a conjunction is the
disjunction of the negations of the component propositoins
Edition by Rosen, 9781259676512, Covering Chapters 1-13 |
Includes Rationales
connectives - ANSWER: logical operators used to form new propositions from two or more existing
propositions
conjunction - ANSWER: "and"; true only when both propositions are true
disjunction - ANSWER: "or"; false only when both propositions are false
exclusive or - ANSWER: true only when exactly one of the propositions is true and false otherwise
implication - ANSWER: conditional statement; "if p, then q" false when p is true and q is false, true
otherwise.
converse of p->q - ANSWER: q->p; equivalent to inverse
contrapositive p->q - ANSWER: not q -> not p; has the same truth value as p->q always
inverse of p->q - ANSWER: not p -> not q; equivalent to converse
equivalent - ANSWER: two compound propositions always having the same truth value
biconditionals (bi-implications; biconditional statements) - ANSWER: if and only if; true only when p
and q have the same truth values; iff
Precedence of logical operators - ANSWER: negation, conjunction, disjunction, conditional,
biconditional
bit - ANSWER: symbol with two possible values, namely 0 and 1
boolean variable - ANSWER: a variable with a value of either true or false
bit string - ANSWER: sequence of zero or more bits; the length of this string is the number of bits in
the string
tautology - ANSWER: a compound proposition that is always true, no matter what the truth values of
the propositional variables that occur in it (emphasis on always)
contradiction - ANSWER: a compound proposition that is always false
contingency - ANSWER: a compound proposition that is always true
logically equivalent - ANSWER: compound propositions that have the same truth values in all possible
cases; when these two propositions, p and q, in the compound proposition p iff q is a tautology.
(emphasis on truth values)
distributive law (disjunction over conjunction) - ANSWER: p V (q^r) = (p v q) ^ (p v r)
De Morgan's Laws - ANSWER: how to negate conjunctions and disjunctions; the negation of a
disjunction is the conjunction of the negation of the components; the negation of a conjunction is the
disjunction of the negations of the component propositoins
