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...
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.
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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