1. - your answers by either writing a sentence or two or by providing a counterexam- ple. Determine if the following statements are true or false and justify (a) The real numbers R with the usual partial order r < y is a well-ordered set. (b) Every quotient group of an abelian group is also abelian. (c) The image under a homomorphism of a group with 6 elements can contain 12 elements. (d) A group of order 20 cannot contain an element of order 7. (c) The set {r EZ|r>0} is a subgroup of (Z. +).

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