Hw5 Problem 7

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Problem 7

Mark each of the following true or false.
(a) The associative law holds in every group.
(b) $\mathbb{Z}_5$ is a cyclic group.
(c) Every group is a subgroup of itself.
(d) In every cyclic group, every element is a generator.
(e) Every set of numbers that is a group under addition is also a group under multiplication.
(f) Every subset of every group is a subgroup under the induced operation.
(g) A subgroup may be defined as a subset of a group.

(a) True
(b) True
(c) True
(d) False
(c) False
(e) False
(f) False
(g) False

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