Exercise · ZW-BINARY-OPERATION-004 · ★☆☆ Basic
The usual subtraction in ℤ is a binary operation because...
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- C. x − y ∈ ℤ for x,y ∈ ℤ
Explanation
Subtraction is a binary operation on ℤ because the difference of two integers is always an integer: x − y ∈ ℤ. It is not commutative, but that is not needed to be a binary operation.
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-005 What are chosen as inputs of a binary operation?
- ZW-BINARY-OPERATION-006 The closure of an operation on G requires that...
- 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?