Exercise · ZW-GROUP-006 · ★★☆ Intermediate

Which structure is a group with the indicated operation?

Choose one option.

Show answer

Explanation

(ℤ,+) is a group. (ℕ,+) has no inverses, (ℤ,·) neither, and (ℝ,·) with 0 included fails because 0 has no multiplicative inverse.

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

\[(G,\ast)\]