A New Operation?

Algebra Level 3

Is ∗ * an operation on the set { n ∈ Z : n ≥ 0 } \{n\in \mathbb Z: n\geq 0\} if it is defined as a ∗ b = ∣ a − b ∣ a*b =|a-b| ?

Hint: Abstract Algebra.

No Yes

Muhammad Rasel Parvej by Muhammad Rasel Parvej , 27, Bangladesh

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1 solution

Yes the given set { n ∈ Z ∣ n ≥ 0 } \large \{ n∈Z | n≥0 \} is closed under the given operation ∗ * . It means, if we take any two elements of the given set and perform their operation according to given definition then we get same element of the set. Hence ∗ * is an operation on set. You can say it is binary operation on given set.

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