Boolean Algebra

In Boolean algebra you represent the logical values true and false by the numbers 1 and 0 respectively.

>>> true
ans = 1
>>> false
ans = 0

and, or, not

The basic operators in logic are and, or and not, these are written using the symbols ∧, ∨ and ¬ respectively. If p and q are statements that are either true or false, then you get the truth table

  • p
  • true
  • true
  • false
  • false
  • q
  • true
  • false
  • true
  • false
  • p ∧ q
  • true
  • false
  • false
  • false
  • p ∨ q
  • true
  • true
  • true
  • false
  • ¬p
  • false
  • false
  • true
  • true

The operators ∧ and ∨ are binary operators, they are applied to two operands. The operator ¬ is an unary operator, it applies to one operand.

In Octave (and most other programming languages) the operators ∧, ∨ and ¬ are written using the symbols &&, || and !; giving the truth table

  • p
  • 1
  • 1
  • 0
  • 0
  • q
  • 1
  • 0
  • 1
  • 0
  • p && q
  • 1
  • 0
  • 0
  • 0
  • p || q
  • 1
  • 1
  • 1
  • 0
  • !p
  • 0
  • 0
  • 1
  • 1

In Octave (and most other programming languages) all numbers that are not 0 are thought of as being true.

>>> a=4.5;
>>> b=0;
>>> (a && b) || !b
ans = 1

Note that you can perform logical operations by using arithmetics.

p && q = pq

p || q = p+q-pq

!p = 1-p

further info:

Fuzzy Logics: This article was published in Scientific American 1993, A Partly True Story, by Ian Stewart

That is true →      ← That is false

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License