Exercise · ZW-GROUP-002 · ★☆☆ Basic

Which structure is a group?

Choose one option.

Show answer
  • A. (ℤ, +)

Explanation

(ℤ, +) satisfies the four axioms: addition is closed and associative, the identity is 0 and the inverse of n is −n. (ℤ, ·) has no inverses, (ℕ, −) is not closed and (ℕ, ·) has no inverses either.

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Review the concept: Group

A group is a nonempty set \(G\) together with an associative binary operation, with an identity element and an inverse for every element.

\[(G,\ast)\]

More practice problems: group

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