Flashcards
Discrete Math Final Exam
Cards in this deck (60)
- 1Universal Statementfor all __,__
- 2Conditional Statementif __, then __
- 3Existential Statement__ exist. There exists __.
- 4seta collection of elements
- 5Set Roster NotationA way of writing a list
- 6Axion of ExtensionAny set is determined entirely by the elements that it contains (not the order in which they're listed or how many times they're listed).
- 7Set Builder Notation{xeS | p(x) is true}
- 8A is a Subset of Bif and only if every element x of A is also an element of B
- 9A is a proper subset of Bif and only if A is a subset of B and there is some b in B that b is not in A.
- 10Ordered Pairany pair of integers (x,y)
- 11The ordered pairs (a,b) and (c,d) are said to be equalif and only if a=c and b=d
- 12Cartesian Product of A and B{(a,b)|a is in A and b is in B}
- 13Relation R from A to BA subset of AxB, set A is the domain and B is the codomain
- 14Function f from a set A to a set BA relation from A to B which satisfies the following 2 conditions:
1.) For all a in A, there exists b in B such that (a,b) is in f
2.) If (a,b) is in f and (a,c) is in f then b=c - 15Statement (or proposition)An assertion which is either true or false, but not both or neither.
- 16Negation of pthe statement which is false when p is true and, true when p is false.
- 17Conjunction of p and qThe statement "p and q"
- 18Disjunction of p and qthe statement "p or q"
- 19Statement Forman expression made up of Statement Variable and logical connectives which becomes a statement when actual statements are substituted for the statement variables.
- 20Two statements are logically equivalentif their truth values are the same.
- 21TautologyA statement form which is always true
- 22Contradictiona statement form which is always false
- 23Which is the hypothesis? "if p then q"p
- 24Contrapositive of the conditional p implies qthe statement ~q implies ~p
- 25Biconditional of two statements p and q"p if and only if q"
- 26iffif and only if
- 27r is a Sufficient Condition for sr implies s
- 28r is a necessary condition for ss implies r
- 29Argumenta list of statements
- 30Argument Forma list of statement forms which becomes and argument when statements are substituted in fr the statement variables.
- 31Premis(es) (or hypothesis)all statements except the last one
- 32conclusionThe last statement
- 33Critical RowAny row in which all the premises are true
- 34Modus Ponensp implies q
p
therefore q - 35Modus Tollensp implies q
~q
therefore ~p - 36Rule of Inferencean argument form which has been previously established as valid.
- 37Predicateis a statement where one or more nouns has been replaced with a variable (called Predicate Variable)
- 38Domainthe set of all possible values of the predicate variables
- 39Truth Setthe set of all elements y of the domain D for which P(y) is true
- 40Universal Quantifierthe clause "for all"
- 41Existential Quantifierthe clause "there exists"
- 42An interger n is Evenif and only if there exists some integer k, such that n=2k
- 43An integer n is Oddif there exists some integer k, such that n=2k+1
- 44An integer n>=2 is Primeif and only if whenever n=jk with j,k in Natural Numbers, either j=n and k=1 or j=1 and k=n
- 45An integer is n is compositeif and only if there exists j,k in Integers with n=jk and 1 < j < n
- 46Constructive proofa proof of a statement with the form "There exists x in D s.t. Q(x)" which asserts that some x in D satisfying Q(x) exists by either a.) Naming the specific x in D for which Q(x) is true, or b.) Describe a procedure where by such an x can be obtained.
- 47counter examplethe statement for all x in D, Q(x)
can be disproved by finding some y in D s.t. ~Q(x) is true - 48rational number rif and only if r=a/b where a,b are integers and b != 0
- 49Real NumberAny number that can be displayed on the number line. Any non imaginary number.
- 50Natural NumberAll positive integers
- 51Integerpositive and negative whole numbers
- 52n divides mn/m
- 53Standard Factored Formgiven any integer n>1 is the decomposition n=p1,p2,pk where p1 < p2...
- 54n div dThe integer quotient obtained when n is divided by d
- 55n mod dThe remainder of dividing n by d
- 56Floor of xthe unique integer n such that n<=x
- 57Ceiling of xthe unique integer n such that n-1
- 58Union of A and B{x in U s.t. (x is in A or x is in B)}
- 59Intersection of A and B{x is in B and x and x is in A}
- 60The Set Difference{x in B s.t. x is not in A
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- Flashcards on Discrete Math Final Exam, created by nordbergr on 18/04/2013.
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