Changes

* Show that <math>\lnot (p \Leftrightarrow q)</math> is equivalent to <math>(\lnot q) \Leftrightarrow p.</math>

* Show that <math>\lnot (p \Leftrightarrow q)</math> is equivalent to <math>(\lnot q) \Leftrightarrow p.</math>

We can translate this into logical graphs by supposing that we have to express everything in terms of negation and conjunction, using parentheses for negation &mdash; that is, "(''x'')" for "not ''x''" &mdash; and simple concatenation for conjunction &mdash; "''xyz''" or "''x y z''" for "''x'' and ''y'' and ''z''".

We can translate this into logical graphs by supposing that we have to express everything in terms of negation and conjunction, using parentheses for negation and simple concatenation for conjunction, thus:

 

The negation <math>\lnot x</math> is written <math>(x).\!</math>

 

The conjunction <math>x \land y</math> is written <math>x y.\!</math>

 

The conjunction <math>x \land y \land z</math> is written <math>x y z.\!</math>

 

Etc.

In this form of representation, for historical reasons called the "existential interpretation" of logical graphs, we have the following expressions for basic logical operations:

In this form of representation, for historical reasons called the "existential interpretation" of logical graphs, we have the following expressions for basic logical operations:

The disjunction "''x'' or ''y''" is written "((''x'')(''y''))".

The disjunction <math>x \lor y</math> is written <math>((x)(y)).\!</math>

This corresponds to the logical graph:

This corresponds to the logical graph: