Welcome guest
You're not logged in.
363 users online, thereof 0 logged in

Definition: Disjunction

Let $$L$$ be a set of propositions with the interpretation $I$ and the corresponding valuation function $[[]]_I$. A disjunction “$$\vee$$” is a Boolean function

$$\vee :=\begin{cases} L \times L & \mapsto L \\ (x,y) &\mapsto x \vee y. \end{cases}$$

defined by the following truth table:

Truth Table of the Conjunction
$[[x]]_I$ $[[y]]_I$ $[[x\vee y]]_I$
$$1$$ $$1$$ $$1$$
$$0$$ $$1$$ $$1$$
$$1$$ $$0$$ $$1$$
$$0$$ $$0$$ $$0$$

We read the disjunction $x\vee y$

“$x$ or $y$”.

Notes

• The disjunction of two propositions is only false if the two propositions are both false. Otherwise, it is true.
• The word or in the natural English language does not correspond to the logical or disjunction. Consider the following example:

$x=$“The month is January”, $y=$“The month is February”

The logical disjunction $x\vee y$ is true if one of $x,y$ (or both) are true, but in English, only one can be true, but never both.

| | | | | created: 2014-06-22 20:32:11 | modified: 2018-05-23 23:08:18 | by: bookofproofs