(e) f (P([5]) - {0}) × (P([8]) - {0}) 4. Write down all the set-partitions P of [5] such that |P| = 2. P([5] × [8]), defined by f(S1, S2) = S1>
(e) f (P([5]) - {0}) × (P([8]) - {0}) 4. Write down all the set-partitions P of [5] such that |P| = 2. P([5] × [8]), defined by f(S1, S2) = S1>
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve Questions NUM 04 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%2F5ec142bd-5beb-4e3e-98c3-4198a23bf7a7%2Fef3gtc_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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
