MATH 110 FINAL EXAM QUESTIONS AND WELL ELABORATED ANSWERS 2025

Conditional Statement - -If, Then statement (A=B) Converse Statement - -Switched conditional statement (B=A) Inverse Statement - -Negative conditional statement (-A=-B) Contrapositive Statement - -Negative and switched conditional statement (-B=-A) What is the most common logical error? - -Assuming that the converse or inverse of a given statement must be true What do Existential Quantifiers indicate? - -The existence of something What are the key phrases/terms for Existential Quantifiers? - -Some, at least, there exists What do Universal Quantifiers indicate? - -That some quality is shared by none of or every item in a set What are some key terms/phrases for Universal Quantifiers? - -All, every, none, no What should be used to negate statements? - -Use the opposite quantifier Counter examples prove what false? - -Statements What is a set? - -A collection of items that can be described in words or with roster notation by using brackets {} What are Natural Numbers? - -All numbers zero through infinity What are Integers? - -All numbers negative infinity through positive infinity What are Rational Numbers? - -The set of all fractions of Integers What are Real Numbers? - -All the numbers on the number line What are Irrational Numbers? - -Any real number that is not rational MATH 110 MATH 110 What is cardinality? - -The number of elements in a set How is cardinality expressed? - -|A| Every set lives within a what? - -Universal Set (U) What is the Compliment of a set, and how is it expressed? - -The set of all elements of the universe that are not elements of A; A' When is set A a Subset of set B? - -If all the elements of set A are also in set B What is the symbol for Subset? - - When is set A a Proper Subset of Set B? - -If A is a subset of B and they are not the same. What is the symbol for a Proper Subset? - - The Empty set is a subset of which set? - -Every set What is the Intersection of sets A and B? - -The set of all elements common between both A and B What is the symbol for Intersection? - - When are sets A and B Disjoint? - -If there are no common elements between sets A and B What is the Union of sets A and B? - -The set of all elements in both A and B What is the symbol for Union? - - What does the Principle in Inclusion and Exclusion (P.I.E) determine? - -The cardinality of multiple Unioned sets What is the formula for P.I.E? - -|A u B| = |A| + |B| - |A n B| How are larger numbers represented in an Additive system? - -By repeating smaller numerals Which two ancient societies used an Additive system? - -The Egyptians and the Romans What is our modern day number system called? - -Hindu-Arabic Which two ancient societies used a Place Value system? - -Babylonians and Mayans MATH 110 MATH 110 What base number was used by the Babylonians? - -60 What base number was used by the Mayans? - -20 What can be used to convert other bases into Hindu-Arabic? - -Expanded form What are the digits of the Hexadecimal system? - -0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F What are the steps to convert a number to Hexadecimal? - -Identify the largest place value and divide for the first digit. Then subtract the powered place Value multiplied by the the digit from the starting number. Repeat What are the step to convert a number into Binary? - -Write down the starting number. If the number is even then divide by 2, if it is odd, subtract 1 then divide by 2. Continue until finished. Then, write a 1 next to the odd numbers and a 0 next to the even numbers. Rewrite from bottom to top In XOR, how does one determine the winning move? - -By getting all zeros What should be done first before finding the factors of a large number? - -Find the square root Perfect squares have a(n) ___ number of factors. - -Odd A number is divisible by 2 if? - -it ends in an even number or 0 A number is divisible by 3 if? - -the sum of its digits is a multiple of 3 A number is divisible by 4 if? - -the last two digits make a multiple of 4 A number is divisible by 5 if? - -it ends in 0 or 5 A number is divisible by 6 if? - -it is divisible by 2 and 3 A number is divisible by 7 if? - -Double the last digit, and subtract from the remaining digits until you can't. If the result is a multiple of 7 then the starting number is A number is divisible by 8 if? - -The last three digits are divisible by 8 A number is divisible by 9 if? - -the sum of digits is divisible by 9 A number is divisible by 10 if? - -it ends in 0 MATH 110 MATH 110 A number is divisible by 11 if? - -the difference between the sum of every other digit is a multiple of 11 What is the Fundamental Theorem of Arithmetic (Prime Factorization)? - -Every composite number can be written as a unique product of prime numbers What are twin primes? - -Prime numbers that are separated by 1 digit What is the sieve of Eratosthenese? - -A method of finding prime numbers by crossing out multiples. numbers left uncrossed are prime How do you find the Greatest Common Factor using the Slide Method? - -Multiply down the side How do you find the Least Common Multiple using the Slide Method? - -Multiply down the side and across the bottom When two or more fractions have the same denominator, which fraction is smaller? - the fraction with the smaller numerator Fractions can be used to represent part of an ___ or ___. - -Area; length When two or more fractions have the same numerator, which fraction is larger? - -The fraction with the smaller denominator What are the three methods for comparing fractions? - -Cross multiply, Bench marking, Converting to decimals What are the steps to converting a repeating decimal into a fraction? - -Determine a repeating pattern;, multiply to make the repeating section a whole number; set up an equation with the whole number and decimal equaling the multiplier; subtract 1 unit from both sides. What are the three models for Addition? - -Joining groups, Joining measures, Moving along the number line What are the four properties of Addition? - -Closure, Commutative, Associative, Identity, What is the Closure property? - -A+B= a whole number