Exercise · ZW-BINARY-OPERATION-009 · ★★☆ Intermediate
Which of these properties is NOT required for an operation to be binary on G?
Choose one option.
Show answer
- B. Associativity
Explanation
Associativity is not part of the definition: a binary operation may or may not satisfy it. The other three are required by the definition: being defined for every pair, the result lying in G, and being a function from \( G \times G \) to \( G \).
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.
\[\ast:G\times G\to G\]
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