QUIZ_ Abstract_ SUBGROUP_1-10

Proper Notation: H is a subset of G

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Proper Notation: H is a subgroup of G, but H is not equal of G

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Proper Notation: H is a subgroup of G

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Proper Notation: H is a subset of G, but H is not equal of G

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It is defined as a subset of a group that follows all necessary conditions to be a group.

• identity

• subgroup

• binary operation

• Closure

• Associative

Which of the following is part of different algebra concept?

• identity

• subgroup

• binary operation

• Closure

• Associative

It shows that ________ as part of subgroup axiom.

• identity

• subgroup

• binary operation

• Closure

• Associative

If a is an element of set H, then a is also an element of set G.

• a ∈ H ⇒ a ∈ G

• a ∈ H = a ∈ G

• a ∈ H ⇒ a ∈ H

• a ∈ G ⇒ a ∈ G

Thus, the result of combining the element 'a' with the identity element 'e' using the operation ⋆ is equal to the result of combining the identity element 'e' with 'a' using ⋆, and both are equal to 'a'.")

• a e = e a = a….

• a ⋆Ξ e = e Ξ a = a….

• a ⋆ e = e ⋆ a = a….

• a + e = e + a = a….

• Multiplication mod 5

• Addition mod 2+3

• addition mode 5