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2. (15 points) For each relation, indicate whether the relation is: • reflexive, anti-reflexive, or neither...
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?...
For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answers for each one. (a) (2 points) The domain is all CPUs. For any CPUs x and y, xRy if x has at least as many cores as y. (b) (2 points) The domain is all people. For any people x and y, xRy if x and y are friends. Assume that everyone is his/her own friend, and that if A...
A topological ordering of G (V, E) is: O An irrefelexive, transitive, anti-symmetric binary relation on V such that E CR ● A reflexive, transitive, symmetric binary relation on V such that E gR O A total ordering on V such that E CR. A partial ordering on V such that E C R A topological ordering of G (V, E) is: O An irrefelexive, transitive, anti-symmetric binary relation on V such that E CR ● A reflexive, transitive, symmetric...
Show work/explain please! 1. (15) Characterize the following relations in terms of whether they are reflexive, irreflexive, symmetric, anti- symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. a. R CRX R with R = {(x,y)|x<y>} b. RCRXR with R= {(x, y)|x3 = y3} C. RSRXR with R = {(x, y) x2 + y2}
(1) For each of the following relations on R, is the relation reflexive? Is it symmetric? Is it transitive? (a)r1={(x, y)∈ R × R | xy= 0} (b) r2={(x, y)∈R×R|x2+y2= 1} (c)r3={(x, y)∈R×R||x−y|<5}
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:
Show your work, please 3. 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) x Ry iff 3 - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) xSy iff 2 = 2y: reflexive: symmetric anti-symmetric: transitive: c) Ty iff zy 30: reflexive: symmetric: anti-symmetric transitive:
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
Question 17 5 pts Let the relation Ron {1,2,3} be given by the following table: R 1 2 3 3 X X X Check all properties that this relation has transitive symmetric reflexive anti-symmetric
For each problem, 3 points will be awarded for the quality of your mathematical writing. Some things to keep in mind here: Make the logical structure of your proof is clear. Is it a proof by contradiction? Contra- positive? If your are proving an equivalence, each direction should be clear Use correct, consistent, and appropriate notation. Define all of the variables you are using. » Write legibly Highlight essential equations or parts of the proof by placing them centered on...