(d) Is M antisymmetric? If not why not? (g) If M is an equivalence relation, what are the equivalence classes of M? (else write "n/a".) (e) Is M transitive? If not why not? (h) If M a partial order relation, then find a chain of M. (else write "n/a".) (f) Is M an equivalence relation, partial order relation, neither, or both?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let ? be the set {x∈ℤ | 2≤x≤7} and relation ? on ? defined by: ??? ⟺ ? and ? have a common factor AND ? ≤ ? .
I Only need E,F,G,& H

2. Let D be the set {XEZ12<x<7} and relation M on D defined by: xMy = x and y have a common
factor AND x < y.
(a) Draw the directed graph of M.
7
(b) Is M reflexive? If not why not?
3
6
(c) Is M symmetric? If not why not?
5
(d) Is M antisymmetric? If not why not?
(g) If M is an equivalence relation, what are the
equivalence classes of M? (else write "n/a".)
(e) Is M transitive? If not why not?
(h) If M a partial order relation, then find a chain of
M. (else write "n/a".)
(f) Is M an equivalence relation, partial
order relation, neither, or both?
2.
Transcribed Image Text:2. Let D be the set {XEZ12<x<7} and relation M on D defined by: xMy = x and y have a common factor AND x < y. (a) Draw the directed graph of M. 7 (b) Is M reflexive? If not why not? 3 6 (c) Is M symmetric? If not why not? 5 (d) Is M antisymmetric? If not why not? (g) If M is an equivalence relation, what are the equivalence classes of M? (else write "n/a".) (e) Is M transitive? If not why not? (h) If M a partial order relation, then find a chain of M. (else write "n/a".) (f) Is M an equivalence relation, partial order relation, neither, or both? 2.
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