6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤ 1.
6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤ 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve Questions NUM 06 in 2 hours and get the thumbs up please show neat and clean work
![3. For each of the functions below, decide whether the function is injective and surjective
(i.e., bijective), or injective but not surjective, or surjective but not injective, or neither
injective nor surjective. If the function is not injective, explain why. If the function is
not surjective, explain why.
(a) f: P([5])→→→→ P([8]), defined by f(S) = SU {6, 7, 8} for SC [5].
(b) f: P([5])→→→→ P([7]), defined by f(S) = SU {5, 6, 7} for SC [5].
(c) f: P([8])→→→→ P([5]), defined by f(S) = Sn [5] for SC [8].
(d) f: P([5]) x P ([8]
P([5] x [8]), defined by f(S₁, S2) = S₁ × S₂.
(e) f (P([5])-{0}) × (P([8]) {0}) →→→ P([5] x [8]), defined by f(S1, S₂) = S₁ × S₂.
4. Write down all the set-partitions P of [5] such that |P| = 2.
5. Write down all the set-partitions P of [6] such that |B| = 2 for all BE P.
6. Write down all the set-partitions P of [5] such that for every BEP, if a E B and
ye B then lyx ≤ 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd580b721-3664-446f-9ceb-e2cc456c38cd%2F8041862b-f220-4012-a058-f811cb3c5e80%2Fqvibgs9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. For each of the functions below, decide whether the function is injective and surjective
(i.e., bijective), or injective but not surjective, or surjective but not injective, or neither
injective nor surjective. If the function is not injective, explain why. If the function is
not surjective, explain why.
(a) f: P([5])→→→→ P([8]), defined by f(S) = SU {6, 7, 8} for SC [5].
(b) f: P([5])→→→→ P([7]), defined by f(S) = SU {5, 6, 7} for SC [5].
(c) f: P([8])→→→→ P([5]), defined by f(S) = Sn [5] for SC [8].
(d) f: P([5]) x P ([8]
P([5] x [8]), defined by f(S₁, S2) = S₁ × S₂.
(e) f (P([5])-{0}) × (P([8]) {0}) →→→ P([5] x [8]), defined by f(S1, S₂) = S₁ × S₂.
4. Write down all the set-partitions P of [5] such that |P| = 2.
5. Write down all the set-partitions P of [6] such that |B| = 2 for all BE P.
6. Write down all the set-partitions P of [5] such that for every BEP, if a E B and
ye B then lyx ≤ 1.
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