NEGATION

By negating something we say that it is not true. If P represents the idea that Jane studies, then PN "translates" Jane does not study or it is false that Jane studies or it is not the case that Jane studies (as well as Jane never studies).

In a two-value logic (one in which we can represent all statements as either 1 or 0), negation is automatically a reciprocal operation: if something is not true, then it is false, and if something is not false then it is true. What this means is that whenever we have the signal N we automatically reverse the value of the letter (variable or signal) in front of it.

Note that N is so far our only unary signal (having one element); all others are binary (having two elements). This is why the count does not change on it.

Special problems come in when we negate expressions with quantifiers. Taking Fx to represent the idea that x is happy, look at the differences in the following:
Everyone is not happy - FNV (the same as no one is happy)
Not everyone is happy - FVN
Not everyone is unhappy - FNVN (the same as someone is happy)
Adding in Gx to represent that x is lucky, we also have
Everyone not happy is unlucky - FNGND
Not everyone happy is lucky - FGDN (the same as there is someone both happy and unlucky)

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