Let X = {1, 2, 3, 4, 5, 6}. Which of the following is a relation on X?O [1, 2], [3, 4]}, {5, 6}}{(1, 2), (3, 4), (5, 6)}O[1, 3, 5)O (12)(34) (56)

Here we have X={1,2,3,4,5,6} We have to determine the relation on X. A relation defines the…

Answered: Let X = {1, 2, 3, 4, 5, 6}. Which of…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question 1 Let A = {11, 22, 33) and B- (11, 22, 33, 44). If the relation R₁ = {(11,11).(22,22), (33,33); and R2 = {(11,11).(11,22), (11,33), (11,44)), then R₁ - R₂ is O (11,11), (11,22), (11,33),(11,44)) O {(22,22),(33,33)} O (11,11),(22,22),(33,33)} O (11,22).(11,33),(11,44)} L A Moving to another question will save this response.
b. Write V as a set of ordered pairs.
3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether R is reflexive, symmetric, and/or transitive. %3D
Let A = {a, b, c, d, and let R be the relation R = {(a, a), (b, b), (c, c), (d, d), (c, b), (a, d), (b, a), (b, d), (c, d), (c, a)}. Is R a total order on A? Yes No Justify your answer. (Select all that apply.) R is antisymmetric. R is not antisymmetric. There exists a chain in R that contains every element of A. There does not exist a chain in R that contains every element of A. R is transitive. R is not transitive. Each element of A exists in R. Each element of A does not exist in R. R is reflexive. R is not reflexive.
Consider the relation R = {(1,1);(2,3);(3,5);(4,7)}. a. Prove that R is a function from {1,2,3,4} to {1,2,3,4;5,6,7}. b. Find a concise formula.
9.25. Let A = {1, 2, 3, 4, 5, 6}. The relation R = {(1,1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1), (5, 5), (6, 2), (6, 3), (6, 6)} is an equivalence relation on A. Determine the distinct equivalence classes.
6. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation xRy when x + y is divisible by 3, then R = O {1, 2), (2, 4)} all of these O {(1, 2), (2, 4), (3, 3)} O {1, 2), (3, 3)}
Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7, 8), (8,9), (9, 9), (7, 7), (8, 8), (7, 9), (9, 7), (9, 8), (8, 7), (0, 0)}. Answer each of the following questions. [8] = [7] = [9] = [0] =
Let X=\{a,b,c,d,e,f\}X={a,b,c,d,e,f} and SS be the relation on XX defined by S = \{ (a,a), (a,b), (a,c),S={(a,a),(a,b),(a,c), (a,d), (a,e), (a,f),(a,d),(a,e),(a,f), (b,b), (b,d), (b,e),(b,b),(b,d),(b,e), (b,f), (c,c), (c,d),(b,f),(c,c),(c,d), (c,e), (c,f), (d,d),(c,e),(c,f),(d,d), (d,e), (d,f), (e,e), (f,f) \}(d,e),(d,f),(e,e),(f,f)}. Is SS a partial order? If so, draw its Hasse diagram. If not, give an example showing why.
let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the inverse of R?

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Let X = {1, 2, 3, 4, 5, 6}. Which of the following is a relation on X? O [1, 2), (3, 4), (5, 6}} O {(1, 2), (3, 4), (5, 6)} O {1, 3, 5) O (12)(3 4) (56)