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MyWikiBiz, Author Your Legacy — Wednesday May 22, 2024
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:* 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 and simple concatenation for conjunction. In this way of assigning logical meaning to graphical forms — for historical reasons called the "existential interpretation" of logical graphs — basic logical operations are given the following expressions:
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. In this way of assigning logical meaning to graphical forms — for historical reasons called the "existential interpretation" of logical graphs — basic logical forms are given the following expressions:
The constant <math>\operatorname{true}</math> is written as a null character or a space.
This corresponds to an unlabeled terminal node in a logical graph. When we are thinking of it by itself, we draw it as a rooted node:
<pre>
@
</pre>
The constant <math>\operatorname{false}</math> is written as an empty parenthesis: <math>(~).</math>
This corresponds to an unlabeled terminal edge in a logical graph. When we are thinking of it by itself, we draw it as a rooted edge:
<pre>
o
|
@
</pre>
The negation <math>\lnot x</math> is written <math>(x).\!</math>
The negation <math>\lnot x</math> is written <math>(x).\!</math>
