Changes

The ''negation'' of a sentence <math>s,\!</math> written as <math>^{\backprime\backprime} \, \underline{(} s \underline{)} \, ^{\prime\prime}</math> and read as <math>^{\backprime\backprime} \, \operatorname{not}\ s \, ^{\prime\prime},</math> is a sentence that is true when <math>s\!</math> is false and false when <math>s\!</math> is true.

The ''negation'' of a sentence <math>s,\!</math> written as <math>^{\backprime\backprime} \, \underline{(} s \underline{)} \, ^{\prime\prime}</math> and read as <math>^{\backprime\backprime} \, \operatorname{not}\ s \, ^{\prime\prime},</math> is a sentence that is true when <math>s\!</math> is false and false when <math>s\!</math> is true.

The ''complement'' of a set <math>Q\!</math> with respect to the universe <math>X\!</math> is denoted by <math>^{\backprime\backprime} \, X\!-\!Q \, ^{\prime\prime},</math> or simply by <math>^{\backprime\backprime} \, {}^{_\sim}\!Q \, ^{\prime\prime}</math> when the universe <math>X\!</math> is determinate, and is defined as the set of elements in <math>X\!</math> that do not belong to <math>Q,\!</math> that is:

The ''complement'' of a set <math>Q\!</math> with respect to the universe <math>X\!</math> is denoted by <math>^{\backprime\backprime} \, X\!-\!Q \, ^{\prime\prime},</math> or simply by <math>^{\backprime\backprime} \, {}^{_\sim} Q \, ^{\prime\prime}</math> when the universe <math>X\!</math> is determinate, and is defined as the set of elements in <math>X\!</math> that do not belong to <math>Q,\!</math> that is:

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" width="90%"

\\

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\text{The fiber of}~ \underline{0} ~\text{under}~ f

\text{The fiber of}~ \underline{0} ~\text{under}~ f

& = & \lnot [| f |]

& = & {}^{_\sim} [| f |]

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\\

& = & f^{-1} (\underline{0})

& = & f^{-1} (\underline{0})