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Abstract Algebra

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Identifying Closed Operations

ABSALG-F3KORG

Identify which of the following operations on the given set are closed?

Select ALL that apply.

A

$\{x\in \mathbb{Z}: x\equiv 0,3 (\textrm{mod } 6)\}$ under addition

B

$\{x\in \mathbb{Z}: x\equiv 0,1 (\textrm{mod } 4)\}$ under multiplication

C

$\{x\in \mathbb{Z}: x\equiv 1,2,3,4 (\textrm{mod } 5)\}$ under addition

D

$\{x\in \mathbb{Z}: x\equiv 1,4 (\textrm{mod } 5)\}$ under multiplication

E

None of the above.