To determine which of the statements is true about subgroups, let's analyze each option:

a. Every group has only one subgroup: This statement is not true. In fact, every group has at least two subgroups - the trivial subgroup containing only the identity element, and the group itself.

b. Every subgroup is a group: This statement is true. By definition, a subgroup is a subset of a group that is itself a group under the same operation.

c. Every subgroup contains only the identity element: This statement is not true. While every subgroup does contain the identity element of the original group, it can also contain other elements.

d. Every group is a subgroup: This statement is not true. A group cannot be a subgroup of itself, as a subgroup must be a proper subset of the original group.

Therefore, the correct answer is b. Every subgroup is a group.

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To determine which of the statements is true about subgroups, let's analyze each option:

a. Every group has only one subgroup: This statement is not true. In fact, every group has at least two subgroups - the trivial subgroup containing only the identity element, and the group itself.

b. Every subgroup is a group: This statement is true. By definition, a subgroup is a subset of a group that is itself a group under the same operation.

c. Every subgroup contains only the identity element: This statement is not true. While every subgroup does contain the identity element of the original group, it can also contain other elements.

d. Every group is a subgroup: This statement is not true. A group cannot be a subgroup of itself, as a subgroup must be a proper subset of the original group.

Therefore, the correct answer is b. Every subgroup is a group.

Knowee AI · Accepted Answer

To determine which of the statements is true about subgroups, let's analyze each option:

a. Every group has only one subgroup: This statement is not true. In fact, every group has at least two subgroups - the trivial subgroup containing only the identity element, and the group itself.

b. Every subgroup is a group: This statement is true. By definition, a subgroup is a subset of a group that is itself a group under the same operation.

c. Every subgroup contains only the identity element: This statement is not true. While every subgroup does contain the identity element of the original group, it can also contain other elements.

d. Every group is a subgroup: This statement is not true. A group cannot be a subgroup of itself, as a subgroup must be a proper subset of the original group.

Therefore, the correct answer is b. Every subgroup is a group.

Which of the following statements is TRUE about subgroups?a.Every group has only one subgroupb.Every subgroup is a groupc.Every subgroup contains only the identity elementd.Every group is a subgroup

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