Switch It Up

Both prefix and postfix notation are more efficient than infix notation because parenthesis need not be used.

Infix To Prefix

∀X{[¬ (P)] ⇒ (X = X)}

¬ ( P )

¬P

X = X

=XX

[¬P]⇒(=XX)

⇒[¬P](=XX)

⇒[¬P](=XX)

⇒¬P=XX

∀X{⇒¬P=XX}

∀X⇒¬P=XX

∀X⇒¬P=XX

Infix To Postfix

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}

W ∈ Z

WZ∈

W = X

WX=

W = Y

WY=

(WX=) ∨ (WY=)

 (WX=)(WY=)∨

 (WX=)(WY=)∨

WX=WY=∨

(WZ∈) ⇔ [WX=WY=∨]

 (WZ∈)(WX=WY=∨)⇔

 (WZ∈)( WX=WY=∨) ⇔

WZ∈WX=WY=∨⇔

∀W{WZ∈WX=WY=∨⇔}

{WZ∈WX=WY=∨⇔}∀W

{WZ∈WX=WY=∨⇔}∀W

WZ∈WX=WY=∨⇔∀W

∃X(WZ∈WX=WY=∨⇔∀W)

∃XWZ∈WX=WY=∨⇔∀W

∃XWZ∈WX=WY=∨⇔∀W

WZ∈WX=WY=∨⇔∀W∃X

∀Y[WZ∈WX=WY=∨⇔∀W∃X]

∀YWZ∈WX=WY=∨⇔∀W∃X

∀YWZ∈WX=WY=∨⇔∀W∃X

WZ∈WX=WY=∨⇔∀W∃X∀Y

∀X{WZ∈WX=WY=∨⇔∀W∃X∀Y}

∀XWZ∈WX=WY=∨⇔∀W∃X∀Y

∀XWZ∈WX=WY=∨⇔∀W∃X∀Y

WZ∈WX=WY=∨⇔∀W∃X∀Y∀X

WZ∈WX=WY=∨⇔∀W∃X∀Y∀X