WGU C959: DISCRETE MATH I EXAM
2025 QUESTIONS AND ANSWERS
When an argument has been translated from English using symbols - ANS Form
Describes an argument when the conclusion is false in a situation with all the hypotheses are
are true - ANS Invalid
Describes an argument when the conclusion is true whenever the hypotheses are all true -
ANS Valid
The final proposition - ANS Conclusion
Each of the propositions within an argument - ANS Hypothesis
Sequence of propositions - ANS Argument
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. -
ANS Two Player Game
A logical expression with more than one quantifier that binds different variables in the same
predicate - ANS Nested Quantifier
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, A logical statement whose truth value is a function of one or more variables - ANS Predicate
The set of all possible values for the variable - ANS Domain of a variable
∀ "for all" - ANS universal quantifier
∀x P(x) - ANS universally quantified statement
For a universally quantified statement, it is an element in the domain for which the predicate is
false. - ANS Counterexample
∃ "there exists" - ANS existential quantifier
∃x P(x) - ANS Existentially quantified statement
Two types are universal and existential - ANS Quantifier
Logical statement including universal or existential quantifier - ANS Quantified Statement
A sequence of steps, each of which consists of a proposition and a justification for an argument
- ANS Logical proof
Has no special properties other than those shared by all elements of the domain -
ANS Arbitrary element
May have properties that are not shared by all the elements of the domain - ANS Particular
2
element
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, Statement that can be proven true - ANS Theorem
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 -
ANS Proof
Statements assumed to be true - ANS Axiom
We don't assume anything about it besides assumptions given in the statement of the theorem
- ANS Generic object
If the domain is small, might be easiest to prove by checking each element individually -
ANS Proof by exhaustion
An assignment of values to variables that shows that a universal statement is false -
ANS Counterexample
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 - ANS Direct proof
A number that can be expressed as the ratio of two integers in which the denominator is non-
zero - ANS Rational number
Proves a conditional theorem of the form p->c by showing that the contrapositive -c->-p is true
- ANS Proof by contrapositve
2k for some integer k - ANS Even integer
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2025 QUESTIONS AND ANSWERS
When an argument has been translated from English using symbols - ANS Form
Describes an argument when the conclusion is false in a situation with all the hypotheses are
are true - ANS Invalid
Describes an argument when the conclusion is true whenever the hypotheses are all true -
ANS Valid
The final proposition - ANS Conclusion
Each of the propositions within an argument - ANS Hypothesis
Sequence of propositions - ANS Argument
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. -
ANS Two Player Game
A logical expression with more than one quantifier that binds different variables in the same
predicate - ANS Nested Quantifier
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, A logical statement whose truth value is a function of one or more variables - ANS Predicate
The set of all possible values for the variable - ANS Domain of a variable
∀ "for all" - ANS universal quantifier
∀x P(x) - ANS universally quantified statement
For a universally quantified statement, it is an element in the domain for which the predicate is
false. - ANS Counterexample
∃ "there exists" - ANS existential quantifier
∃x P(x) - ANS Existentially quantified statement
Two types are universal and existential - ANS Quantifier
Logical statement including universal or existential quantifier - ANS Quantified Statement
A sequence of steps, each of which consists of a proposition and a justification for an argument
- ANS Logical proof
Has no special properties other than those shared by all elements of the domain -
ANS Arbitrary element
May have properties that are not shared by all the elements of the domain - ANS Particular
2
element
Page
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, Statement that can be proven true - ANS Theorem
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 -
ANS Proof
Statements assumed to be true - ANS Axiom
We don't assume anything about it besides assumptions given in the statement of the theorem
- ANS Generic object
If the domain is small, might be easiest to prove by checking each element individually -
ANS Proof by exhaustion
An assignment of values to variables that shows that a universal statement is false -
ANS Counterexample
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 - ANS Direct proof
A number that can be expressed as the ratio of two integers in which the denominator is non-
zero - ANS Rational number
Proves a conditional theorem of the form p->c by showing that the contrapositive -c->-p is true
- ANS Proof by contrapositve
2k for some integer k - ANS Even integer
3
Page
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