The binary connective darr is called the Peirce arrow, named for American philosopher Charles Peirce $($not

for the antique automobile$).$ The truth table for darr is given here. In Chapter $8$ we will see that this truth table

represents the NOR gate

Show that every compound statement is equivalent to a statement

using only the connective darr. $($Hint: See Exercise $51.)$ Include all compund statements

$($

and

$,$

$$or

$,$

$$xor$,$ implication, equivelance

$)$

$.$ Make sure to explain the rules you use in each conversion.