CMA201 Discrete Mathematics

Dear Students, I have some notes shared at the end of this page. Let me know if there is any problem.

Sets

Power Sets

Question

Let A = {x,y,z}. Find P(A).

Answer

P(A) = {{},{x},{y},{z},{x,y},{x,z},{y,z},{x,y,z}}

Methods of Proofs

Proofs

Question

Write down the inverse and contrapositive of:

“If I am lazy, I will fail”.

Answer

Let

p : lazy

q : fail

If I am lazy, I will fail

p → q

Inverse:

~p → ~q

If I am not lazy, I will not fail.

Contrapositive:

~q → ~p

If I do not fail, I am not lazy

Graph Theory

Isomorphic Graphs

Items to check when trying to show that a pair of graphs are isomorphic are:

1. The number of vertices

2. The number of components

3. The number of edges

4. The degree sequence

5. The length of the shortest path between pairs of vertices with a given degree

6. The length of the longest path in the graph

Regards,