Provide an ADT specification for \(\texttt{Boolean}\) type. By definition, a Boolean is either \(\texttt{true}\) or \(\texttt{false}\). The negation (\(\texttt{Not}\)) of a Boolean is also a Boolean. The \(\texttt{and}\) and \(\texttt{or}\) between two Booleans is also a Boolean.

Difficulty level
This exercise is mostly suitable for students 
Type  Boolean

Uses 

Parameter

FUCNTIONS
	true 	:		    -> Boolean
	false 	: 	            -> Boolean
	not 	: Boolean	    -> Boolean
	and 	: Boolean x Boolean -> Boolean
	or 	: Boolean x Boolean -> Boolean

AXIOMES Let X be a variable
[1] not(true) = false
[2] non(false) = true
[3] and(true, X) = X
[4] and(false, X) = false
[5] or(true, X) = true
[6] or(false, X) = X

EXAMPLES
not(or(true , (and(false,not(true))))) ==
not(or(true , (and(false,false))))  (by [1])
== not(or(true , false))  (by [4])
== not(true) (by [5]) == false (by [1]).
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