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Question 3: a) Let P be the set of prime numbers, O the set of odd numbers, E the set of even numbers and S the set of square numbers. Describe, as simple as possible, the set: i) PNs ii) P-0 iii) PNE

Question 3: a) Let P be the set of prime numbers, O the set of odd numbers, E the set of even numbers and S the set of square numbers. Describe, as simple as possible, the set: i) PNs ii) P-0 iii) PNE

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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Question 3: a) Let P be the set of prime numbers, O the set of odd numbers, E the set of even numbers and S the set of square numbers. Describe, as simple as possible, the set: i) PNs ii) P -0 PNE iii) b) Let S be the set of square numbers, N, the set of natural numbers and O, the set of odd numbers. Consider the functions f and g defined as: f:S - N, f(s) = vs g:N - 0, g(n) = 2n + 1 i) Is fog possible? If so, compute fo g and its image set. If not, explain in details why not. ii) Is go f possible? If so, compute go f and its image set. If not, explain in details why not. iii) Between f°g and g • f decide which one is a bijection and prove it.
Transcribed Image Text:Question 3: a) Let P be the set of prime numbers, O the set of odd numbers, E the set of even numbers and S the set of square numbers. Describe, as simple as possible, the set: i) PNs ii) P -0 PNE iii) b) Let S be the set of square numbers, N, the set of natural numbers and O, the set of odd numbers. Consider the functions f and g defined as: f:S - N, f(s) = vs g:N - 0, g(n) = 2n + 1 i) Is fog possible? If so, compute fo g and its image set. If not, explain in details why not. ii) Is go f possible? If so, compute go f and its image set. If not, explain in details why not. iii) Between f°g and g • f decide which one is a bijection and prove it.
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