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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 statements, compound statements, connectives, negation, conditional statements, truth tables, sets, and number systems. Designed to help students prepare for the exam by providing a thorough understanding of the course 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: When are ordered pairs equal? - =Answer>> The are equal provided that their first components are equal and their second components are equal. What is a statement? - =Answer>> It is a declarative sentence that is either true or false, but not simultaneously. What is a compound statement? - =Answer>> It is formed by combining two or more statements. What is a component statement? - =Answer>> It is the statement that makes up a compound statement. List examples of connectives. - =Answer>> And, or, not, if...then. Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
What is the negation of P - =Answer>> Direct Statement (Valid) - =Answer>> If P then Q P
Q Contrapositive (Valid) - =Answer>> If P then Q -Q
-P Transitive (Valid) - =Answer>> If P then Q If Q then R
If P then R Disjunctive Syllogism (Valid) - =Answer>> P V Q -Q / -P
P / Q Fallacy of Converse (Invalid) - =Answer>> If P then Q Q
P Fallacy of Inverse (Invalid) - =Answer>> If P then Q -P
-Q Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
False Chains - =Answer>> If P then Q / If P then Q If P then R / If R then Q
If Q then R / If P then R Disjunctive Fallacy - =Answer>> P V Q / P V Q P / Q
-Q / -P Natural/Counting Numbers - =Answer>> 1,2,3, Elipsis - =Answer>> ... inductive reasoning - =Answer>> Specific --> general. Starts with a conclusion. Counterexample - =Answer>> any example that proves a conditional statement false. Only one exception is necessary to prove a conjecture false. If no counterexample is found, then the conjecture is neither proven or disproven. Deductive reasoning - =Answer>> General --> Specific. Hypothesis Well defined set - =Answer>> A set is well defined if its contents can be clearly determined. Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
one-to-one correspondence - =Answer>> every element must have a match. Empty set - =Answer>> a set with no elements, ∅ { } U - =Answer>> Universal set. Items inside the rectangle may be divided into subsets of U. Disjoint Sets - =Answer>> No elements in common Proper Subset - =Answer>> A proper subset of a set is a subset of that is not equal to. In other words, if is a proper subset of , then all elements of are in but contains at least one element that is not in. For example, if A = { 1 , 3 , 5 } then B = { 1 , 5 } is a proper subset of Complement of a set - =Answer>> The complement of set A, symbolized is the set of all elements in the universal set that are not in set A. A' Intersection - =Answer>> The intersection of sets A and B, symbolized A ∩ B, is the set containing all the elements that are common to both set A and set B. "AND" Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
Union - =Answer>> The union of sets A and B, symbolized A ∪B, is the set containing all the elements that are members of set A or of set B (or of both sets.) "OR" Exactly two - =Answer>> All intersections, except for intersections of all 3 Statement - =Answer>> A sentence that can be judged either true or false Subset - =Answer>> ⊆ If any and only if all elements of set A are also elements of set B. Smaller set is the subset, Must include all original subsets. Aristotle - =Answer>> Father of logic Connectives - =Answer>> and, or, if, then Exclusive or - =Answer>> one or the other, but not both Inclusive or - =Answer>> One or the other, but not both Simple statement - =Answer>> A sentence that conveys only one idea and can be assigned a truth value Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
Disjunction: True when either or both are true If p is true, then ~p is false If p is false, then ~ is true Set - =Answer>> A collection of objects. Elements - =Answer>> The objects or members of a set. Natural/Counting Numbers - =Answer>> {1,2,3,4...} Whole Numbers - =Answer>> {0,1,2,3,4...} Includes zero. Intergers - =Answer>> {...,-3.-2,-1,0,1,2,3,...} All numbers including positive, negative and zero. Rational Numbers - =Answer>> May be written as a terminating decimal (0.25) or a repeating decimal (0.333...) Irrational Numbers - =Answer>> Decimal representations never terminate and never repeat like pi (3.14...) Real Numbers - =Answer>> Can be expressed as a decimal. Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
Cardinal Number - =Answer>> The number of elements in a set. Finite Set - =Answer>> If the cardinal number of a set is a particular whole number. Infinite Set - =Answer>> Whenever a set is so large that it's cardinal number is not found among the whole numbers. Equal Set - =Answer>> -The sets contain identical elements. -Every element of set A is an element of set B and every element of set B is an element of set A. Equivalent Sets - =Answer>> Contain the same # of elements, but not necessarily the same elements. Universal Set - =Answer>> The set of all possible elements from which subsets are formed. Universal Set - =Answer>> The set of all possible elements from which subsets are formed. Need Writing 🤔Help? We've Got You Covered! ✍ 100% NO A I or Plagiarism Guaranteed🤔
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