# Discrete Mathematics/Selected problems

The problems in the texts you have seen are for you to ensure that you understand the concepts and ideas explored. They are not intended to be very difficult, but understandably they are not very challenging.

Questions here are intended for you to further use the ideas you have learnt to answer some more difficult questions. Some questions are relatively straightforward, some of these questions depend on different sections of this discrete mathematics text, some of these questions are meant to be examination-style questions.

Do not be discouraged by the increase in difficulty - hints are sometimes available, and you will be able to increase your problem solving skills!

## Set theory questions

These questions depend on your knowledge of Set theory.

1. We have the sets A={0, 1, 3, 4, 5, 7}, B = {2, 4, 5, 8, 9}, C = {1, 4, 9, 11, 21}. Write the elements of the set ${\displaystyle (A\cap C)\cup B}$ Check your solution: [1]
2. Using the set identities, simplify ${\displaystyle (A\cap B)'\cup A}$
3. (Hint provided) Prove the set ${\displaystyle \{x|x/2\in \mathbb {N} \}}$ is not a subset of ${\displaystyle \{y|y/4\in \mathbb {N} \}}$
4. (Hint provided) Prove the set ${\displaystyle \{3n+5|n\in \mathbb {N} \}}$ is not a subset of ${\displaystyle \{6k+6|k\in \mathbb {N} \}}$