Suppose that we have a large software project divided into several files. Let F be the...
Suppose that we have a large software project divided into several files. Let F be the set of files, and let R be the relation on F where fRg if g depends on f. That is, f must be compiled before g. Note that the dependency might not be direct — g might depend on f through some intermediary files h, j etc.. For the purposes of this question, assume that there is at least one file.
a) Is R reflexive, irreflexive, both or neither? Explain why.
b) Is R symmetric, anti-symmetric, both or neither? Explain why.
c) Is R transitive? Explain why.
d) Is R an equivalence relation a partial ordering, or a strict partial ordering? Explain why.
e) If R is an equivalence relation, describe the equivalence classes. Otherwise, if R is a (strict) partial ordering, is it also a (strict) total ordering? Explain why.
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Suppose that we have a large software project divided into
several files. Let F be the...
Show work/explain please! 1. (15) Characterize the following relations in terms of whether they are reflexive,...
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}
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined...
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(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...
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4. Let S be the set of continuous function f: [0;1) ! R. Let R be...
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Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given...
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QUESTION 10 The equality relationon any set S is: A total ordering and a function with an inverse. An equivalence relation and also function with an inverse. A function with an inverse, and an equiva...
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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}
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order...
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...
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(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...
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