Page 21, Exercise 4

ADT Boolean is objects:
TRUE, FALSE ∈ Boolean and the Boolean== the usual boolean operation.
where == return TRUE if tw set elements are the same, and TRUE otherwise.

Boolean not(x) ::= if (x) return TRUE
   return FALSE
Boolean and(x,y) ::= if(not(x)) return FALSE
    if (not(y)) return FALSE
    return TRUE
Boolean or(x, s) ::= if(x) return TRUE
    if (y) return TRUE
    return FALSE
Boolean xor(x, s)

::= if(and(not(x), not(y))) return FALSE
    if (and(x, y)) return FALSE
    return TRUE
Boolean implies(x, s) ::= if (and(x, y)) return TRUE
    if (and(not(x),not(y))) return TRUE
    return FALSE
Boolean equivalent(x, s) ::= if(and(not(x), not(y))) return TRUE
    if (and(x, y)) return TRUE
    return FALSE

end Set