Recall that a prime number is an integer that is greater than 1 and has no positive integer divisors other than 1 and itself. (In particular, 1 is not prime.) A relation P is defined on Z as follows. For every m, nEZ, m Pn a prime number p such that p | m and p | n. (a) Is P reflexive? |---Select--- ☑, because when m = ---Select--- then there ---Select--- ✓ prime number p such that p | m. (b) Is P symmetric? |---Select--- ☑, because for m = ---Select--- and n = ---Select--- ' if p is a prime number such that p ---Select--- m and p---Select--- n, then p-Select--- n and p-Select--- m. (c) Is P transitive? |---Select--- ☑, because, for example, when m = 12, n = 15, and o = , then there is a prime number that ---Select--- both m and n, and there is a prime number that ---Select--- both n and o, and ---Select--- prime number that ---Select--- both m and o.

Recall that a prime number is an integer that is greater than 1 and has no positive integer divisors other than 1 and itself. (In particular, 1 is not prime.) A relation P is defined on Z as follows. For every m, nEZ, m Pn a prime number p such that p | m and p | n. (a) Is P reflexive? |---Select--- ☑, because when m = ---Select--- then there ---Select--- ✓ prime number p such that p | m. (b) Is P symmetric? |---Select--- ☑, because for m = ---Select--- and n = ---Select--- ' if p is a prime number such that p ---Select--- m and p---Select--- n, then p-Select--- n and p-Select--- m. (c) Is P transitive? |---Select--- ☑, because, for example, when m = 12, n = 15, and o = , then there is a prime number that ---Select--- both m and n, and there is a prime number that ---Select--- both n and o, and ---Select--- prime number that ---Select--- both m and o.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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