## Nothing going on here, move along…

### Truth tables and equations

Proposition – A declaration sentence that is either true or false

Compound proposition – A proposition which can be broken down into small propositions, eg.

If it is sunny outside then I walk to work; otherwise

I drive, and if it is raining then I carry my umbrella.

This can be broken down into: Sunny outside, walk to work, drive to work, raining, carry umbrella.

Tautology – When a column in a truth table is completely true

Contradiction – When a column in a truth table is completely false

Contingency – When a column in a truth table is neither a tautology nor a contradition

These statements are both true

p Λ T = p (p and true = p)

p ν F = p (p or false = p)

Different meanings of some symbols

Λ = and = x

V = or = +

T = 1

F = 0

Predicate logic

Q = Relationship

Let Q(x,y) denote:

x = y + 3

In this equation the x is dependent, as in dependent on the the equation to exist, the y is independant, if any other part of the equation isn’t there it remains the same.