Exercise · ZW-GROUP-010 · ★☆☆ Basic
If an operation has an identity e, what must hold?
Choose one option.
Show answer
- A. e∗a=a∗e=a for all a
Explanation
If e is the identity, e ∗ a = a ∗ e = a must hold for every a in the set. The other options ask for things that do not define the identity.
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
- ZW-GROUP-001 Which list contains the axioms of a group?
- ZW-GROUP-002 Which structure is a group?
- ZW-GROUP-003 Why is (ℤ, ·) not a group?
- ZW-GROUP-004 What is the identity of (ℤ, +)?
- ZW-GROUP-005 What is the inverse of 3 in (ℤ, +)?
- ZW-GROUP-006 Which structure is a group with the indicated operation?
- ZW-GROUP-007 ℕ=\0,1,2,…\ with the usual addition is not a group because...
- ZW-GROUP-008 The identity of a group must...