To determine which of the options is NOT a requirement for a subset to be a subgroup, we will analyze each option one by one.

a. It contains the identity element of the group: This is a requirement for a subset to be a subgroup. The identity element must be present in the subset.

b. It is closed under the group operation: This is also a requirement for a subset to be a subgroup. The subset must be closed under the group operation, meaning that if you perform the operation on any two elements within the subset, the result must also be in the subset.

c. It is closed under the inverse operation: This is another requirement for a subset to be a subgroup. The subset must be closed under the inverse operation, meaning that for every element in the subset, its inverse must also be in the subset.

d. It is closed under addition: This option is NOT a requirement for a subset to be a subgroup. The group operation mentioned in option b could be any operation, not necessarily addition. So, the subset does not have to be closed under addition specifically.

Therefore, the correct answer is d. It is closed under addition.

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To determine which of the options is NOT a requirement for a subset to be a subgroup, we will analyze each option one by one.

a. It contains the identity element of the group: This is a requirement for a subset to be a subgroup. The identity element must be present in the subset.

b. It is closed under the group operation: This is also a requirement for a subset to be a subgroup. The subset must be closed under the group operation, meaning that if you perform the operation on any two elements within the subset, the result must also be in the subset.

c. It is closed under the inverse operation: This is another requirement for a subset to be a subgroup. The subset must be closed under the inverse operation, meaning that for every element in the subset, its inverse must also be in the subset.

d. It is closed under addition: This option is NOT a requirement for a subset to be a subgroup. The group operation mentioned in option b could be any operation, not necessarily addition. So, the subset does not have to be closed under addition specifically.

Therefore, the correct answer is d. It is closed under addition.

Knowee AI · Accepted Answer

To determine which of the options is NOT a requirement for a subset to be a subgroup, we will analyze each option one by one.

a. It contains the identity element of the group: This is a requirement for a subset to be a subgroup. The identity element must be present in the subset.

b. It is closed under the group operation: This is also a requirement for a subset to be a subgroup. The subset must be closed under the group operation, meaning that if you perform the operation on any two elements within the subset, the result must also be in the subset.

c. It is closed under the inverse operation: This is another requirement for a subset to be a subgroup. The subset must be closed under the inverse operation, meaning that for every element in the subset, its inverse must also be in the subset.

d. It is closed under addition: This option is NOT a requirement for a subset to be a subgroup. The group operation mentioned in option b could be any operation, not necessarily addition. So, the subset does not have to be closed under addition specifically.

Therefore, the correct answer is d. It is closed under addition.

Which of the following is NOT a requirement for a subset to be a subgroup?a.It contains the identity element of the groupb.It is closed under the group operationc.It is closed under the inverse operationd.It is closed under addition

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