Exercise · ZW-BINARY-OPERATION-006 · ★★☆ Intermediate
The closure of an operation on G requires that...
Choose one option.
Show answer
- A. a ∗ b ∈ G for all a,b∈G
Explanation
Closure requires a ∗ b ∈ G for all a, b ∈ G. It does not ask for commutativity, inverses or for the result to be zero.
Review the concept: Binary operation
A binary operation on a set G is a function that takes any two elements of G and returns an element of G.
\[\ast:G\times G\to G\]
More practice problems: binary operation
- ZW-BINARY-OPERATION-001 A binary operation on G must be a function...
- ZW-BINARY-OPERATION-002 Which is a binary operation on ℤ?
- ZW-BINARY-OPERATION-003 To be a binary operation, the result must...
- ZW-BINARY-OPERATION-004 The usual subtraction in ℤ is a binary operation because...
- ZW-BINARY-OPERATION-005 What are chosen as inputs of a binary operation?
- ZW-BINARY-OPERATION-007 Associativity is written as...
- ZW-BINARY-OPERATION-008 Which rule is a binary operation on ℤ?
- ZW-BINARY-OPERATION-009 Which of these properties is NOT required for an operation to be binary on G?