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# Give a recursive definition ofa) the set of odd positive

ISBN: 9780073383095 37

## Solution for problem 24E Chapter 5.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 24E

Problem 24E

Give a recursive definition of

a) the set of odd positive integers.

b) the set of positive integer powers of 3.

c) the set of polynomials with integer coefficients.

Step-by-Step Solution:
Step 1 of 3

MATH​ ​103​ ​Chapter​ ​2​ ​Notes Set​ ​​​ ollection​​ f​ ​objects​ ​well​ ​defined ● {A} Element​ - ​​​ ember​ ​of​ ​a​ et ● ∈ ● 1​ ​​∈​ ​​A ● 5​ ​​∉​ ​​A Sets​ ​are​​ esignated​ ​by: ● Word​ ​description​ ​(1st​ ​3​ l​ etters​ ​of​ ​the​ ​alphabet) ● Listing​ ​ r​ ​roster​ ,​ ,​ ​c​ ​} ● Set​ ​builder​ ​notation​ ​{​ ​x​ ​|​ ​x​ ​is​ ​the​ ​first​ ​3​ ​letters​ ​of​ ​the​ ​alphabet​ ​} Empty​ ​or​ ​ ull​ et ● Ø​ ​​ r​ ​​ ​{​ ​​ ​​ ​} ● NEVER​​ ​​uses​ ​{​ ​Ø​ ​} Cardinal​ ​Number​​ ​-​ ​​number​ ​of​ ​elements​ ​in​ ​a​ ​set​ ​(how​ ​many) ● If​ ​​ ​A​ ​=​ ​{​ ​1,​ ​2,​ ​3,​ ​4​ ​},​ ​then​ ​​ ​n(A)​ ​=​ ​4​ ​​ ​(because​ ​there​ ​are​ ​four​ ​numbers,​ ​or​ ​elements,​ ​in​ ​that set) Finite​

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Step 3 of 3

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Give a recursive definition ofa) the set of odd positive