Addition and multiplication are internal composition laws on ℕ, and intersection and union are internal composition laws on 𝒫(ℕ).
For functions from E to E, composition is an internal composition law because composing two functions E→E produces another function E→E.
Internal means the result stays in E; external operations can leave E.
1. Which condition makes a binary operation an internal composition law on a set E?
2. Why is composition an internal composition law for functions from E to E?
3. Which equation expresses that an internal law * is commutative?
What is an internal composition law on a set E?
It is an application mapping pairs to elements in E.
Which operations are internal composition laws on ℕ?
Addition and multiplication are internal composition laws on ℕ.
Which operations are internal composition laws on 𝒫(ℕ)?
Intersection and union are internal composition laws on 𝒫(ℕ).
Why is composition of functions from E to E an internal composition law?
Because composing two functions E→E produces another function E→E.
When is an internal law * commutative?
When for every pair in .
When is an internal law * associative?
When for every triple in .
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