Show that the set 4Z U 5Z is not a subring of the integer ring Z:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show that the set 4Z U 5Z is not a subring of the integer ring Z:

Expert Solution
Given conditions.

Z = { ....., -3, -2, -1, 0, 1, 2, 3, ..... }.

4Z = { ...., -8, -4, 0, 4, 8, .... }.

5Z = { ...., -10, -5, 0, 5, 10, .... }.

So, 4Z U 5Z = { ...., -10, -8, -5, -4, 0, 4, 5, 8, 10, ..... }.

We have to prove that the set 4Z U 5Z is not a subring of the integer ring Z.

 

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