DISCRETE MATHEMATICS WITH
APPLICATIONS COMPREHENSIVE EXAM
SCRIPT VERIFIED QUESTIONS AND
SOLUTIONS GRADED APLUS
●● Conclusion
Answer: the assertion at the end of the sequence. The final statement or
statement form
●● Premises
Answer: the preceding statements before the conclusion.
●● Valid
Answer: Both arguments are called ________ in the sense that if their
premises are true, then their conclusion must also be true.
●● Statement (or Proposition)
Answer: is a sentence that is true or false, but not both.
●● ~
Answer: denotes "not"
,●● ^
Answer: denotes "and"
●● v
Answer: denotes "or"
●● Order of Operations
Answer: " ~ " is performed first, then "v or ^"
●● Truth Values
Answer: must either be true or false
●● Negation
Answer: If p is a statement variable, the _________ of p is "not p" or "It
is not the case that p" and is denoted ~p. It has opposite truth value from
p: if p is true, ~p is false; if p is false, then ~p is true.
●● Conjunction
Answer: If p and q are variables, the __________ of p and q is "p and
q," denoted p ^ q. It is true when, and only when, both p and q are true.
If either p or q is false, or if both are false, p ^ q is false.
●● Disjunction
, Answer: If p and q are statement variables, the __________ of p and q is
"p or q," denoted (p v q). It is true when either p is true, or q is true, or
both p and q are true; it is false only when both p and q are false.
●● Statement Form (or Propositional Form)
Answer: is an expression made up of statement variables (such as p, q,
and r) are logical connectives (such as ~, ^, v) that becomes a statement
when actual statements are substituted for the component statement
variables. The truth table for a given statement displays the truth values
that correspond to all possible combinations of truth values for its
component statement variables.
●● Exclusive "or"
Answer: the statement "p or q" means "p or q but not both" or "p or q
and not both q and q," which translates into symbols as (p v q) ^ ~(p ^
q). Denoted as ⊕
●● Logically Equivalent
Answer: 1) Two statement forms are called ___________ if, and only if,
they have identical truth values for each possible substitution of
statements for their statement variables.
2) Two statement are called ____________ if, and only if, they have
____________ forms when identical component statement variables are
used to replace identical component statements.
APPLICATIONS COMPREHENSIVE EXAM
SCRIPT VERIFIED QUESTIONS AND
SOLUTIONS GRADED APLUS
●● Conclusion
Answer: the assertion at the end of the sequence. The final statement or
statement form
●● Premises
Answer: the preceding statements before the conclusion.
●● Valid
Answer: Both arguments are called ________ in the sense that if their
premises are true, then their conclusion must also be true.
●● Statement (or Proposition)
Answer: is a sentence that is true or false, but not both.
●● ~
Answer: denotes "not"
,●● ^
Answer: denotes "and"
●● v
Answer: denotes "or"
●● Order of Operations
Answer: " ~ " is performed first, then "v or ^"
●● Truth Values
Answer: must either be true or false
●● Negation
Answer: If p is a statement variable, the _________ of p is "not p" or "It
is not the case that p" and is denoted ~p. It has opposite truth value from
p: if p is true, ~p is false; if p is false, then ~p is true.
●● Conjunction
Answer: If p and q are variables, the __________ of p and q is "p and
q," denoted p ^ q. It is true when, and only when, both p and q are true.
If either p or q is false, or if both are false, p ^ q is false.
●● Disjunction
, Answer: If p and q are statement variables, the __________ of p and q is
"p or q," denoted (p v q). It is true when either p is true, or q is true, or
both p and q are true; it is false only when both p and q are false.
●● Statement Form (or Propositional Form)
Answer: is an expression made up of statement variables (such as p, q,
and r) are logical connectives (such as ~, ^, v) that becomes a statement
when actual statements are substituted for the component statement
variables. The truth table for a given statement displays the truth values
that correspond to all possible combinations of truth values for its
component statement variables.
●● Exclusive "or"
Answer: the statement "p or q" means "p or q but not both" or "p or q
and not both q and q," which translates into symbols as (p v q) ^ ~(p ^
q). Denoted as ⊕
●● Logically Equivalent
Answer: 1) Two statement forms are called ___________ if, and only if,
they have identical truth values for each possible substitution of
statements for their statement variables.
2) Two statement are called ____________ if, and only if, they have
____________ forms when identical component statement variables are
used to replace identical component statements.
