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MyWikiBiz, Author Your Legacy — Tuesday November 26, 2024
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The negation <math>\lnot x</math> is written <math>(x).\!</math>
The negation <math>\lnot x</math> is written <math>(x).\!</math>
This corresponds to the logical graph:
<pre>
x
o
|
O
</pre>
The conjunction <math>x \land y</math> is written <math>x y.\!</math>
The conjunction <math>x \land y</math> is written <math>x y.\!</math>
This corresponds to the logical graph:
<pre>
x y
O
</pre>
The conjunction <math>x \land y \land z</math> is written <math>x y z.\!</math>
The conjunction <math>x \land y \land z</math> is written <math>x y z.\!</math>
This corresponds to the logical graph:
<pre>
xyz
O
</pre>
Etc.
Etc.
</pre>
</pre>
The disjunction "''x'' or ''y'' or ''z''" is written "((''x'')(''y'')(''z''))".
The disjunction <math>x \lor y \lor z</math> is written <math>((x)(y)(z)).\!</math>
This corresponds to the logical graph:
This corresponds to the logical graph:
Etc.
Etc.
The implication "''x'' ⇒ ''y''" is written "(''x'' (''y'')), which can be read "not ''x'' without ''y''" if that helps to remember the form of expression.
The implication <math>x \Rightarrow y</math> is written <math>(x (y)),\!</math> which can be read "not <math>x\!</math> without <math>y\!</math>" if that helps to remember the form of expression.
This corresponds to the logical graph:
This corresponds to the logical graph:
</pre>
</pre>
Thus, the equivalence "''x'' ⇔ ''y''" has to be written somewhat inefficiently as a conjunction of to and fro implications: "(''x'' (''y''))(''y'' (''x''))".
Thus, the equivalence <math>x \Leftrightarrow y</math> has to be written somewhat inefficiently as a conjunction of two implications: <math>(x (y)) (y (x)).\!</math>
This corresponds to the logical graph:
This corresponds to the logical graph:
( (p (q)) (q (p)) ) = (p ( (q) )) ((p)(q))
( (p (q)) (q (p)) ) = (p ( (q) )) ((p)(q))
</pre>
</pre>
