WGU C959 DISCRETE MATH ACTUAL EXAM
PAPER 2026 QUESTIONS WITH VERIFIED
ANSWERS AND COMPLETE SOLUTIONS
⩥ Invalid. Answer: Describes an argument when the conclusion is false
in a situation with all the hypotheses are are true
⩥ Valid. Answer: Describes an argument when the conclusion is true
whenever the hypotheses are all true
⩥ Conclusion. Answer: The final proposition
⩥ Hypothesis. Answer: Each of the propositions within an argument
⩥ Argument. Answer: Sequence of propositions
⩥ Two Player Game. Answer: In reasoning whether a quantified
statement is true or false, it is a useful way to think of the statement in
which universal and existential compete to set the statement's truth
value.
⩥ Nested Quantifier. Answer: A logical expression with more than one
quantifier that binds different variables in the same predicate
,⩥ Predicate. Answer: A logical statement whose truth value is a function
of one or more variables
⩥ Domain of a variable. Answer: The set of all possible values for the
variable
⩥ universal quantifier. Answer: ∀ "for all"
⩥ universally quantified statement. Answer: ∀x P(x)
⩥ Counterexample. Answer: For a universally quantified statement, it is
an element in the domain for which the predicate is false.
⩥ existential quantifier. Answer: ∃ "there exists"
⩥ Existentially quantified statement. Answer: ∃x P(x)
⩥ Quantifier. Answer: Two types are universal and existential
⩥ Quantified Statement. Answer: Logical statement including universal
or existential quantifier
,⩥ Logical proof. Answer: A sequence of steps, each of which consists of
a proposition and a justification for an argument
⩥ Arbitrary element. Answer: Has no special properties other than those
shared by all elements of the domain
⩥ Particular element. Answer: May have properties that are not shared
by all the elements of the domain
⩥ Theorem. Answer: Statement that can be proven true
⩥ Proof. Answer: Series of steps, each of which follows logically from
assumptions, or from previously proven statements, whose final step
should result in the statement of the theorem being proven
⩥ Axiom. Answer: Statements assumed to be true
⩥ Generic object. Answer: We don't assume anything about it besides
assumptions given in the statement of the theorem
⩥ Proof by exhaustion. Answer: If the domain is small, might be easiest
to prove by checking each element individually
, ⩥ Counterexample. Answer: An assignment of values to variables that
shows that a universal statement is false
⩥ Direct proof. Answer: The hypothesis p is assumed to be true and the
conclusion c is proven to be a direct result of the assumption; for
proving a conditional statement
⩥ Rational number. Answer: A number that can be expressed as the ratio
of two integers in which the denominator is non-zero
⩥ Proof by contrapositve. Answer: Proves a conditional theorem of the
form p->c by showing that the contrapositive -c->-p is true
⩥ Even integer. Answer: 2k for some integer k
⩥ Odd integer. Answer: 2k+1 for some integer k
⩥ Irrational number. Answer: Real number that cannot be written as a
fraction
⩥ Proof by contradiction. Answer: Starts by assuming that the theorem
is false and then shows that some logical inconsistency arises as a result
of this assumption
PAPER 2026 QUESTIONS WITH VERIFIED
ANSWERS AND COMPLETE SOLUTIONS
⩥ Invalid. Answer: Describes an argument when the conclusion is false
in a situation with all the hypotheses are are true
⩥ Valid. Answer: Describes an argument when the conclusion is true
whenever the hypotheses are all true
⩥ Conclusion. Answer: The final proposition
⩥ Hypothesis. Answer: Each of the propositions within an argument
⩥ Argument. Answer: Sequence of propositions
⩥ Two Player Game. Answer: In reasoning whether a quantified
statement is true or false, it is a useful way to think of the statement in
which universal and existential compete to set the statement's truth
value.
⩥ Nested Quantifier. Answer: A logical expression with more than one
quantifier that binds different variables in the same predicate
,⩥ Predicate. Answer: A logical statement whose truth value is a function
of one or more variables
⩥ Domain of a variable. Answer: The set of all possible values for the
variable
⩥ universal quantifier. Answer: ∀ "for all"
⩥ universally quantified statement. Answer: ∀x P(x)
⩥ Counterexample. Answer: For a universally quantified statement, it is
an element in the domain for which the predicate is false.
⩥ existential quantifier. Answer: ∃ "there exists"
⩥ Existentially quantified statement. Answer: ∃x P(x)
⩥ Quantifier. Answer: Two types are universal and existential
⩥ Quantified Statement. Answer: Logical statement including universal
or existential quantifier
,⩥ Logical proof. Answer: A sequence of steps, each of which consists of
a proposition and a justification for an argument
⩥ Arbitrary element. Answer: Has no special properties other than those
shared by all elements of the domain
⩥ Particular element. Answer: May have properties that are not shared
by all the elements of the domain
⩥ Theorem. Answer: Statement that can be proven true
⩥ Proof. Answer: Series of steps, each of which follows logically from
assumptions, or from previously proven statements, whose final step
should result in the statement of the theorem being proven
⩥ Axiom. Answer: Statements assumed to be true
⩥ Generic object. Answer: We don't assume anything about it besides
assumptions given in the statement of the theorem
⩥ Proof by exhaustion. Answer: If the domain is small, might be easiest
to prove by checking each element individually
, ⩥ Counterexample. Answer: An assignment of values to variables that
shows that a universal statement is false
⩥ Direct proof. Answer: The hypothesis p is assumed to be true and the
conclusion c is proven to be a direct result of the assumption; for
proving a conditional statement
⩥ Rational number. Answer: A number that can be expressed as the ratio
of two integers in which the denominator is non-zero
⩥ Proof by contrapositve. Answer: Proves a conditional theorem of the
form p->c by showing that the contrapositive -c->-p is true
⩥ Even integer. Answer: 2k for some integer k
⩥ Odd integer. Answer: 2k+1 for some integer k
⩥ Irrational number. Answer: Real number that cannot be written as a
fraction
⩥ Proof by contradiction. Answer: Starts by assuming that the theorem
is false and then shows that some logical inconsistency arises as a result
of this assumption
