3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. a) The relation Ron Z where aRb means a = b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive? Yes or No Yes or No Yes or No Yes or No b) The relation R on the set of all people where aRb means that a is taller than b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive?...
Question 2 For each of the following relations R, determine (and explain) whether R is: (1) reflexive (2) symmetric (3) antisymmetric (4) transitive (a) R-(x, y):x +2y 3), defined on the set A 10, 1,2,3) (b) R-I(x, y): xy 4), defined on the set A (0,1,2,3,4 (c) R-(x, y): xy 4), defined on the set A-0,,2,3)
Question 2 For each of the following relations R, determine (and explain) whether R is: (1) reflexive (2) symmetric (3) antisymmetric (4) transitive (a)...
Please explain in detail!!
4. If binary relation R is given by matrix [1 0 1 0 1 101 м, 1 1 1 0 1 1 0 1 determine, if R is: (a) reflexive (b) symmetric (c) antisymmetric (d) transitive?
Suppose that R61,3), (1, 4), (2, 3), (2,4), (3,1), (3,4)), Determine which of these statements are correct Check ALL correct answers below A. R6 is symmetric B. R1 is reflexive C. R4 is symmetric D. R3 is transitive E. R3 is reflexive F. R2 is reflexive G. R2 is not transitive H. R4 is antisymmetric I. R1 is not symmetric J. R5 is transitive K. R4 is transitive L. Rs is not reflexive M. R3 is symmetric
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if a) x + y = 0 b) x= ±y. c) x-y is a rational number. d) = 2y. e) xy ≥ 0. f) xy = 0. g) x=l. h) r=1 or y = 1
2. (12) True or False Let R {(1, 2), (2, 3), (, 1, (2, 2), (3, 3), (, 3) (1) R is reflexive. (2) R is transitive (3) R is symmetric. (4) R is antisymmetric.
Relations - No Proofs! Determine (no proof needed!) whether each of the following relations R, S, T on the set of real numbers is reflexive, symmetric, antisymmet- ric, and/or transitive. a) « Ry iff r - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) Sy iff r = 2y reflexive: symmetric: anti-symmetric: transitive: c) <Ty iff zy < 0: reflexive: symmetric: anti-symmetric: transitive:
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
10. Represent the following relation R on the set (. t,s t) as a digraph and as a acro-ooe ati eachi b) Circle the properties of R antisymmetric itive 2 peins) reflexive symmetric 떼 1 find the symmetric and transitive closures ofS (4 pirtepi 1 c)If Ms-10 Transitive Closure Symmetric Closure_-
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...