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
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.