Discrete Mathematics with
Applications (Chapter 1 & 2)
Questions with complete solution
2026
Argument - correct answer ✔is a sequence of statements aimed at demonstrating the truth of an
assertion.
Conclusion - correct answer ✔the assertion at the end of the sequence. The final statement or
statement form
Premises - correct answer ✔the preceding statements before the conclusion.
Valid - correct answer ✔Both arguments are called ________ in the sense that if their premises are
true, then their conclusion must also be true.
Statement (or Proposition) - correct answer ✔is a sentence that is true or false, but not both.
~ - correct answer ✔denotes "not"
^ - correct answer ✔denotes "and"
v - correct answer ✔denotes "or"
Order of Operations - correct answer ✔" ~ " is performed first, then "v or ^"
, Truth Values - correct answer ✔must either be true or false
Negation - correct 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 - correct 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 - correct 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) - correct 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" - correct 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 - correct 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 (Chapter 1 & 2)
Questions with complete solution
2026
Argument - correct answer ✔is a sequence of statements aimed at demonstrating the truth of an
assertion.
Conclusion - correct answer ✔the assertion at the end of the sequence. The final statement or
statement form
Premises - correct answer ✔the preceding statements before the conclusion.
Valid - correct answer ✔Both arguments are called ________ in the sense that if their premises are
true, then their conclusion must also be true.
Statement (or Proposition) - correct answer ✔is a sentence that is true or false, but not both.
~ - correct answer ✔denotes "not"
^ - correct answer ✔denotes "and"
v - correct answer ✔denotes "or"
Order of Operations - correct answer ✔" ~ " is performed first, then "v or ^"
, Truth Values - correct answer ✔must either be true or false
Negation - correct 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 - correct 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 - correct 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) - correct 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" - correct 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 - correct 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.
