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- I need help on this questionState the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric, and Transitive. Then construct three small worlds showing, respectively, that a relation can be Reflexive and not Symmetric, Symmetric and not Transitive, and Reflexive and not Transitive. Finally, for each of the three small worlds that you construct, give an example of a relation in ordinary language that works like the relation in the small world you built. That is, for your first small world, give an ordinary language example of a relation that is Reflexive and not Symmetric.1. We are given the sets S and V: S = {Anne, Theo} V {studies, runs, meditates} = (a) Find the Cartesian Product of S and V: S x V (b) A relation R. is a subset of the Cartesian product. Create such a subset RC (S X V) with three elements.
- 6. Q6; Relations (a) Define relations S and R on the set A = {a, b, c, d} as follows: {(a, b), (b, c), (c, d), (b, b)}, S = R = {(b, a), (c, c), (a, c), (d, b)}. i. Find So S, So R, R-o So R. Is R-lo SoR= S ? ii. Determine which of S, R, So R, S-1 or R-1 is a function. (b) Let R = {(x, y) E R × R : 115. Let C = {(2n + 1)³:n € R } and D = {2n + 1:n € R}. What is the relation between these two sets? State and prove your answer.Choose the answerQuestion 1 Let A be the set A = {3,4, 8, 9, 12, 24, 54). Determine whether the following relationships are (1) transitive, (2) reflexive, and (3) symmetric or anti-symmetric. Provide the set for each relation on the set A. a. R = {(a, b) a divides b} b. R = {(a,b)| aFor any sets A B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.A={1,2,3,4,5,6} and consider the following 3 subsets of A. A = {1,3,5}; A2 = Let {2, 4, 6}; A3 = {3, 6}.9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b), (a, c)} is a relation on S. Which of the properties reflexive, symmetric and transitive does the relation R possess? Justify your answers.Suppose A and B are two finite sets such that |B| = |A| - 1 and the number of relations on A is 512. Determine: |B|: Number of relations from B to A:Recommended textbooks for youAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill EducationAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education