Problem Set #2: Introduction to Abstract Algebra.
As you work through these problems, think about the logical steps you are using. You should know if your proof is correct or not if you have a reason for every step.
1: Determine if the follow maps are onto and/or 1:1:
such that
.
such that
.
such that
.
such that
.
2: Prove that if
and
are nonempty sets, then the function
given by the relation
is a bijection.
3: Suppose the set
is finite.
- Prove that if
is an onto map, then
is a one-to-one map.
- Prove that if
is a one-to-one map, then
is an onto map.
4: Suppose that the set
is not finite.
- Provide a counter example to the proposition that if
is an onto map, then
is a one-to-one map.
- Provide a counter example to the proposition that if
is a one-to-one map, then
is an onto map.