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A comprehensive set of review questions and answers for mgf 1106 mathematics for liberal arts exam 1. It covers key concepts such as sets, logic, and number theory, offering valuable insights and practice for students preparing for the exam. Organized in a clear and concise manner, making it easy for students to navigate and understand the material.
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Course Title and Number: MGF 1106 Mathematics for liberal Arts 1 Exam Exam Title: MGF 1106 1 Exam Exam Date: Exam 2024- 2025 Instructor: [Insert Instructor’s Name] Student Name: [Insert Student’s Name] Student ID: [Insert Student ID]
180 minutes
Read All Instructions Carefully and Answer All the Questions Correctly Good Luck: Set - =Answer>> Any collection or group of objects Element - =Answer>> individual object in a set description of a set - =Answer>> B is a set of natural numbers greater than 4 roster form - =Answer>> B=(5,6,7...) set builder notation - =Answer>> B=(xIxEN and x>4) B=(x is the set of all x such that E...) equal sets - =Answer>> if and only if they contain identical elements in any order cardinal number - =Answer>> n(A) number of elements in set Set - =Answer>> Collection or group of objects (ex: favorite color) Well-defined set - =Answer>> Constant set (ex: multiples of 3) Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
n(A) - =Answer>> Number of elements in A (cardinal number of A) IMPORTANT FORMULA #1 - =Answer>> n(A∪B) = n(A) + n(B) - n(A∩B) How many components in a simple statement? - =Answer>> 1 How many components in a compound statement? - =Answer>> More than 1 ∧ - =Answer>> conjunction: and, but ∨ - =Answer>> disjunction: or ~ - =Answer>> not, it is not the case that ~(p∧q) - =Answer>> ~p ∨ ~q ~(p∨q) - =Answer>> ~p ∧ ~q Negation of "all" - =Answer>> Some are not Negation of "never/none" - =Answer>> Some are What number do counting numbers not include? - =Answer>> 0 List the components of the compound statement: 9 + 8 ≥ 16 - =Answer>> 9 + 8 = 16 9 + 8 > 16 Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
⊂ - =Answer>> proper subset ⊆ - =Answer>> subset A⊆A - =Answer>> Any set is a subset of itself A⊄A - =Answer>> A proper subset of A is any subset strictly smaller than A ∅⊂A - =Answer>> The empty set is a subset (and proper subset) of any set A equivalent sets - =Answer>> if and only if they have the same cardinal number empty set - =Answer>> no elements universal set - =Answer>> contains all the elements subset - =Answer>> sideways u with underline proper subset - =Answer>> sideways u without underline Demorgans laws for sets - =Answer>> (AUB)'=A' and B' (A and B)'=A'UB' complement - =Answer>> opposite of the set intersection - =Answer>> and, what is in both union - =Answer>> or, everything in the sets Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
negation does what - =Answer>> change the true value negation with qualifiers - =Answer>> how many all some more at least one possibly all negation to "all are" - =Answer>> some are not negation to "none are" - =Answer>> some are conjunction truth table cheat - =Answer>> only true if both true disjunction truth table cheat - =Answer>> only false if both false conditional truth table cheat - =Answer>> always true unless TF in that order biconditional truth table cheat - =Answer>> only true if TT or FF equivalent statements - =Answer>> if and only if both statements have same final values for truth table demorgans laws for statements - =Answer>> -(p or q)<---
-p and -q -(p and q)<--->-p or -q converse - =Answer>> q-->p Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
inverse - =Answer>> -p-->-q contrapositive - =Answer>> -q-->-p equivalent statement to conditional - =Answer>> contrapositive equivalent statement to converse - =Answer>> inverse parts of a symbolic argument - =Answer>> premise and conclusion how is an argument valid? - =Answer>> if and only if the conclusion is the only conclusion that logically follows assume premise is true testing the validity of and argument - =Answer>> write in symbolic form write as compound statement and do truth table not valid unless tautology Law of detachment - =Answer>> P--->q p
q Law of contrapostion - =Answer>> P--->q -q
-p Law of Syllogism - =Answer>> P--->q q--->r
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divisible by 6 if - =Answer>> the number is divisible by 2 or 3 divisible by 8 if - =Answer>> last 3 digits are divisible by 8 divisible by 9 if - =Answer>> sum of digits is divisible by 9 divisible by 10 if - =Answer>> last digit is 0 prime numbers - =Answer>> natural numbers that have two positive factors, itself and 1 composite numbers - =Answer>> natural numbers that have at least one number besides itself and 1 minimun number of factors that must be checked to see if a number is prime - =Answer>> p^2>n prime factorization - =Answer>> branching or separated by bars gcd methods - =Answer>> list factors prime factorization euclidian algorithm(long division) lcm methods - =Answer>> list multiples prime factorization theorem gcd(a,b)xlcm(a,b)=axb rational numbers - =Answer>> numbers that can be expressed as a quotient of two integers Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
finding fraction of repeating decimal steps - =Answer>> 1. let n=.6 repeating 2.get decimal to left of bar 3.multiply both sides by 10 4.subtract 2 from 3 denseness property - =Answer>> a set is dense if and only if between two numbers there exists a third number always pathagorean theorem - =Answer>> a^2+b^2=c^ irrational numbers - =Answer>> real number who's decimal is not nonterminating and non repeating product rule for radicals - =Answer>> square root of a and b equals the square root of a times square root of b division rule for radicals - =Answer>> square root of a and b equals the square root of a divided by the square root of b mixed number to improper fraction - =Answer>> take big number and multiply by denominator and then add the numerator 5 1/4= 21/ improper fraction to mixed number - =Answer>> do long division whole number is big number and remainder is numerator over the original denominator 7/4=1 3/ Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
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