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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.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 7CA
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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.
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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