2.4. Discrete Structures

Try these first

1. 1.

   Define mathematical proof.

   Hint

   Think about how you prove something means to show it is true.

2. 2.

   What is a set?

   Hint

   Consider how sets are often represented in mathematics.

3. 3.

   What is the definition of a set?

   • A collection of distinct objects.
   • A mathematical equation.
   • A graph of relations.

   Hint

   Think about how sets are used in mathematics.

4. 4.

   True or False: Proof by contradiction assumes the opposite of what you want to prove.

   • True
   • False

   Hint

   Consider how indirect proofs work.

5. 5.

   Using proof by induction, show that for every n >= 1, the sum of the first n even numbers is n(n+1).

   Hint

   Establish your base case and the inductive hypothesis first.

6. 6.

   Discuss how graph theory can improve route optimization in logistics.

   Hint

   Consider how connections in a network can help in finding efficient paths.