Maths / Logic and Modelling – CNF

This is going to be the first post I’m going to write that is valid for BOTH year 1 and year 2. Just in case you get confused as to who should be reading it 😉

CNF is short for Conjunctive Normal Form. A formula is in CNF if it is True (T) or False ( _|_ ) or a conjunction of disjunctions:

What is Logic?

This is post is going to help you better understand and grasp the concepts behind Propositional Logic (PL). In general, PL is the study  of logical operators and their use in correct arguments.

A better Example

Let’s take a look at another example, this time lets use:

Maths – Induction (part 1)

A = for all.    E = there exists ]

The Principles of Induction

Firstly, welcome to Induction. The one thing in Discrete Maths that I hear a heck of a lot of people complaining about! – So don’t worry, you’re not the only one 🙂

Composition of Functions

Say we have 2 functions:

• fR ——> S1
• gS2 —–> T

Maths – Functions (part 1)

In Discrete Maths, ‘Functions’ have 3 features:

1. Source (S) , or more commonly known as the Domain
2. Target (T), or more commonly known as the CoDomain
3. Behaviour, which is what the function does as it transforms the source (input) into the target (output)

Relations

If we have two sets, A and B, we can refer to the ‘Cartesian Product’ as being A x B.  This means that if A = {1, 2, 3} and B = {a, b, c}, then A x B = {1a, 1b, 1c, 2a, 2b, 2c, 3a, 3b, 3c}.  It’s the set of all pairs of values where the first is from A and the second  is from B.

A relation from A to B is a subset of A x B.  A relation can be said to connect values together, in a way, showing a relationship between them.