Problem 25. Suppose that the relation "being similar to" is an equivalence relation onMnxn (F). That is, for every A, B, C € Mnxn (F),(1) A is similar to itself.(2) If A is similar to B, then B is similar to A.(3) If A is similar to B and B is similar to C, then A is similar to C.1

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Answered: Problem 25. Suppose that the relation…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 7CA

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Problem 9For the following equivalence relation describe the corresponding partition without anyredundancy or reference to the name of the relation. Let ∼be the relation on R−{0}definedby x ∼y if and only if xy > 0, for all x, y ∈R−{0}.
Problem 7. Which of the following relations ∼ on Z is an equivalence relation? Explain your answer, and for each relation that is an equivalence relation, give the set Z/ ∼ of all equivalence classes. 4.x∼yiffx=yorx=−y.
Problem 1: A. In the piggy bank I have 90 coins. 20 quarters, some pennies, and 30 half dollars. How many different ways can these coins be put into a row? B. Find all possibilites of a relation on {4, 5, 6} that is reflexive and transitive, but not symmetric. Discrete Math
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PROBLEM1 Instruction: Prove that the relation is an equivalence relation. For x, y ∈ R say x is congruent to y modulo Z if x−y is an integer, that is x − y ∈ Z.
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Draw a directed graph diagram for relation S on {0, 1, 2, 3,4}, where TSy iff x + y = 4
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I know that in order to show an equivalence relation I need to check for (1) reflexivity, (2) Symmetry, and (3) transitivity. I just cant figure out how to prove those things for this problem. (Problem attached.)
Question 1: Give examples for sets with 3, 4, 7 elements. Write 5 statements about those sets which include the relations ∈, ∉, ⊂, ⊄. Determine the truth of each statement. (Make sure you use all the sets and given relations.) Question 2: Write 10 statements which include the relations ∈, ∉, ⊂, ⊄ for the sets ℕ, ℤ, ℚ, ℝ, ∅. Determine the truth of each statement. (Make sure you use all the sets and given relations.) Question 3: Calculate the following expressions by giving the action on the number line. a) 7 − 15 = b) −2 − 9 = c) −6 + 8 = d) 11 − 6 = e) 9 + 5 = Question 4: Calculate the following expressions. Show all the details of your work. a) −2 + 4(7 − 9) = b) −2(4 − 7) + 9 = c) −2[(4 − 7) + 9] =

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Big Ideas Math A Bridge To Success Algebra 1: Stu…

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ISBN:

9781680331141

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HOUGHTON MIFFLIN HARCOURT

Publisher:

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