Changes

And so on.

And so on.

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.

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 what it means.

This corresponds to the logical graph:

This corresponds to the logical graph:

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Thus, the equivalence <math>x \Leftrightarrow y</math> has to be written somewhat inefficiently as a conjunction of to and fro implications:  <math>(x (y)) (y (x)).\!</math>

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:

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Putting all the pieces together, the problem given amounts to proving the following equation, expressed in the forms of logical graphs and parenthetical parse strings, respectively:

Putting all the pieces together, showing that <math>\lnot (p \Leftrightarrow q)</math> is equivalent to <math>(\lnot q) \Leftrightarrow p</math> amounts to proving the following equation, expressed in the forms of logical graphs and parse strings, respectively:

 

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

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