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C959 Discrete Math I| 305 questions and answers.
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  • WGU C959 - Discrete Math
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Form When an argument has been translated from English using symbols Invalid Describes an argument when the conclusion is false in a situation with all the hypotheses are are true Valid Describes an argument when the conclusion is true whenever the hypotheses are all true Co...

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  • 13 de octubre de 2023
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  • 2023/2024
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  • c959 discrete math i

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  • Oxford University (OX)
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  • WGU C959 - Discrete Math
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C959: Discrete Math I 305 questions and
answers
Form - answer When an argument has been translated from English using symbols



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



Indirect proof - answer Another name for a proof by contradiction



Proof by cases - answer For a universal statement, it breaks the domain into different classes and gives a
different proof for each class. All of the domain must be covered.



Parity - answer Whether a number is odd or even

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