Discrete Mathematics Answers

‘A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’.

Using Rules of Inference, can you show step by step that this argument is valid?
NOT(IF p THEN q) AND p = NOT(q)

‘A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’. Is it true or false? give reasons.

Let R be a relation on ℤ given by xRy if and only if x²-y² is divisible by 3. Show that this relation is an equivalence relation and find its corresponding equivalence classes.

Using the method of "searching for a falsifying truth assignment" prove the
De Morgan's law

1. To access your Webwork account you are required to input the correct user-
name and password. Suppose the you have autoll for your username and
are only required to input your password. You are granted \access" to your
account if you input the correct password otherwise access is \denied".
(a) Use only variables p and q to make up a propositional formula for how
the system responds. based on the password you input.

If A= (a,b,c) then generate P(A) and 3 partition sets for A.

1. Construct a proof for the five color theorem for every planar graph.
2. Discuss how efficiently Graph Theory can be used in a route planning project for a vacation trip from Colombo to Trincomalee by considering most of the practical situations (such as mileage of the vehicle, etc.) as much as you can. Essentially consider the two fold,
- Routes with the shortest distance (Quick route travelling by own vehicle)
- Route with the lowest cost

1. State the Dijkstra’s algorithm for a directed weighted graph with all non-negative edge weights.

2. Function converts Fahrenheit temperatures into Celsius. What is the function for opposite conversion?