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(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>

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 39E
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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.
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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