Math 360, Fall 2018, Assignment 7

Do not imagine that mathematics is hard and crabbed and repulsive to commmon sense. It is merely the etherealization of common sense.

- Lord Kelvin

Read:

1. Section 5.

Carefully define the following terms, then give one example and one non-example of each:

1. Substructure (of a binary structure).
2. Subgroup (of a group).

Carefully state the following theorems (you need not prove them):

1. Theorem giving conditions for a subset of a group to be a subgroup.
2. Theorem concerning unions and intersections of subgroups.

Solve the following problems:

1. Section 5, problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, and 13.

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