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Finite Mathematics

Quiz yourself by thinking what should be in each of the black spaces below before clicking on it to display the answer.
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Question
Answer
Inductive Reasoning   Observation of Specific Examples  
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Deductive Reasoning   Proving a specific conclusion from one or more general statements  
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Rounding   If digit to the right is 5 or more, round the digit up 1 and change everything to the right to zeros. If less than five, don't change and make everything to the right zeros  
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Roster Method   Listing items of a set between curly braces {}  
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Set Builder Notation   B={x|x is all of the days of the week that begin with T}  
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The Empty Set   {} or 0 with a line through it.  
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ϵ   Is an Element of  
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ϵ with a / through it   Is NOT an element of  
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Natural Numbers   Counting Numbers starting with 1 and going to infinity  
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Cardinality of a set n(A)   The number of distinct elements of a set. Said as n of A  
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Equivalence of a set   Two (or more) sets have the same cardinal number  
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Finite Set   If it is the empty set or if its cardinal number is a natural number  
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Set Equality   If both sets have the same elements, regardless of order or repetition, they are equal.  
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A sideways U above half an equals sign B   means A is a subset of B  
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A sideways U above half an equals sign, with a / through it   means A is NOT a subset of B  
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Sideways U (no line)   Proper Subset A is a proper subset of B if it is a subset of B and is NOT equal to B  
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Number of Subsets with n elements   2^n  
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Number of Proper Subsets   (2^n)-1  
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Statement   Can be true or false, but not both simultaneously  
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All A are B   There are no A that are not B  
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Some A are B   There exists at least one A that is B  
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No A are B   All A are not B  
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Some A are not B   Not all A are B  
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All A are B - negated   Some A are not B  
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Some A are B - negated   All A are not B  
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AND   ^  
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OR   v  
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NOT   ~  
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But Yet Nevertheless   ALL AND  
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IF-THEN   -->  
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Antecedent   Comes before the connective -->  
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Consequent   Comes after the connective -->  
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If p then q   p-->q  
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q if p   p-->q  
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p is sufficient for q   p-->q  
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q is necessary for p   p-->q  
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p only if q   p-->q  
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only if q, p   p-->q  
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<-->   If and only if  
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p if and only if q   p<-->q  
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q if and only if p   p<-->q  
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If p then q and if q then p   p<-->q  
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p is necessary and sufficient for q   p<-->q  
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q is necessary and sufficient for p   p<-->q  
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parenthesis, bi-conditional, conditional, conjunctive, negation   order of operations for logic  
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commas indicate grouping in written logic   She is happy and wealthy, only if she is married. (h^w)<-->m  
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Conjunction Truth   Only true when both simple statements are true.  
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Disjunction Falsity   Only false when both simple statements are false  
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Conditional Falsity   Only false when the antecedent is true and the consequence is false  
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Biconditional Truth   Only true when both sides are the same.  
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Factor = Divisor   If the remainder is 0, then x is divisible by y, y is a factor of x and y is a divisor of x  
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Prime Number   >1 and divisible only by itself and 1  
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Composite Number   >1 and divisible by itself, 1 and at least 1 other number  
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Fundamental Theorem of Arithmetic   Every composite number can be expressed as the product of prime numbers in 1 and only 1 way.  
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Relatively prime   Greatest Common Divisor is 1  
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Find Greatest common divisor   1. Factor both numbers completely. 2. Find the factors common to both and use the smallest exponent 3. Multiply those numbers  
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Find Least Common Multiple   1. Factor the numbers 2. Use EVERY factor, with the largest exponent only 3. Multiply these numbers  
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Whole Numbers   0 and natural numbers  
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Integers   0 and natural numbers and negatives of natural numbers  
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Rational Numbers   All numbers that can be expressed as a fraction where both numerator and denominator are integers and the denominator is not 0  
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Repeating Decimal as a fraction   1. n= repeating decimal 2. Multiply it by 10 for one repeat, 100 for two, etc 3. Subtract equation 1 from equation 2 4. Solve for N  
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a/b * c/d   (a*c)/(b*d)  
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(a/b)/(c/d)   (a*d)/(b*d)  
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Irrational Numbers   Numbers whose decimals are neither terminating or repeating. sqrt 2 and Pi  
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simplifying square roots   sqrt of 18 = sqrt 9 * sqrt 2 therefore sqrt 18 =3sqrt2 and division works the same way.  
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Real Numbers   Set of Rational Numbers and Irrational Numbers  
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Exponent Rules   To multiply, add To divide subtract Raising to a power, multiply  
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Closure   Every possible result of the operation exists in the set of numbers included in the operation  
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Commutative Property   Doesn't matter what order you do it in.  
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Associative Property   (A#B)#C = A#(B#C)  
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Identity Property   Operation on any object in the set with the Identity Element results in the original element  
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Inverse Property   When operated on with the particular operation, it results in the identity element for that set.  
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Identity Element of Addition   0  
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Identity Element of Multiplication   1  
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Identity Element of Division   1  
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Identity Element of Subtraction   0  
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Group   Closed (under the operation given) Is Associative under the operation Has an identity element each element has an inverse in the set  
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congruent in a modular system   a (3 equals) b (mod m) a and b give same remainder when divided by m  
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Modular addition   Modulo M system add a + b. If it's less than M, that's the answer If it's greater than M, the answer is the remainder when it is divided by M  
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Equivalent Graphs   Have the same number of vertices connected in the same way  
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Degree of vertex   Number of edges connected to the vertex. A loop counts as two.  
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Euler Path   Travels through every edge once and only once  
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Euler Circuit   Travels through every edge once and only once and begins and ends on the same vertex  
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Rules of Euler Graphs   1. If it has exactly two odd vertices, it has 1 path that starts at one odd vertex and ends at the other. 2. If it has all even vertices, it has a least one euler circuit and it can begin on any vertex 3. If more than two odd vx, no path or circuit  
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Hamilton Path   Passes through each vertex of a graph once and only once  
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Hamilton Circuit   Passes through each vertex and begins and ends at the same vertex  
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Number of Hamilton-Circuits   (n-1)!  
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