Exercise · ZW-BINARY-OPERATION-008 · ★★☆ Intermediate
Which rule is a binary operation on ℤ?
Choose one option.
Show answer
- C. a∗b=a+b+1
Explanation
a ∗ b = a + b + 1 is defined for every pair of integers and gives an integer. The others fail: 1/(a − b) does not exist if a = b and is not an integer in general, √(a + b) is not always an integer, and a rule that is not defined for a = b is not an operation on all of ℤ.
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
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