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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
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