Question

Consider the binary operations on X, a*b = a+b+4, for a, b e X. It satisfies the properties of​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

It satisfies the properties of Abelian.

Explanation:

Since * closed operation, a*b belongs to X. Hence, it is an abelian group.

More information about Abelian group:

Abelian groups satisfy all the following properties:

$1.Closure: For \: all a,b∈Ga.b∈G$

$2.Associativity: For \: all a,b,c∈G , a⋅(b⋅c)=(a⋅b)⋅c$

$3.Identity \: Element: There \: exists e∈G such \: that \: for \: all a∈G, a⋅e=e⋅a=a.$

4.$Inverse \: Element: For \: all a∈G, there \: exists b∈G such \: that a⋅b=b⋅a=e.$

5.$Commutative: For \: \: all a,b∈G, a⋅b=b⋅a$

A thing to note is that stands for a binary operation which can be multiplication, addition, or composition. The first 4 properties are from the definition of a group. The only thing that makes Abelian groups different from other groups is that the Abelian group has the commutative property. Sometimes, the Abelian group is also called a commutative group.