(defun if-then-truth-table ()
    (list (if nil nil) (if nil t) (if t nil) (if t t)))

(defun if-then-else-truth-table ()
    (list (if nil nil) (if nil t) (if t nil) (if t t)))

(defun if-then-else-truth-table ()
    (list (if nil nil nil) (if nil nil t) (if nil t nil) (if nil t t)
	  (if t nil nil) (if t nil t) (if t t nil) (if t t t)))

(defun if-then-else-equiv-truth-table ()
    (list (if-then-else nil nil nil) (if-then-else nil nil t)
	  (if-then-else nil t nil) (if-then-else nil t t)
	  (if-then-else t nil nil) (if-then-else t nil t)
	  (if-then-else t t nil) (if-then-else t t t)))

(defun and-truth-table ()
    (list (and nil nil) (and nil t) (and t nil) (and t t)))

(defun or-truth-table ()
    (list (or nil nil) (or nil t) (or t nil) (or t t)))

(defun if-then-else-t-truth-table ()
    (list (if nil nil t) (if nil t t) (if t nil t) (if t t t)))

(defun implies-truth-table ()
    (list (implies nil nil) (implies nil t) (implies t nil) (implies t t)))

(defun iff-truth-table ()
    (list (iff nil nil) (iff nil t) (iff t nil) (iff t t)))

(defun implies (p q)
    (if p q t))

(defun iff (p q)
    (and (implies p q) (implies q p)))

(defun if-then-else (p q r)
    (or (and p q) (and (not p) r)))

(defun test-truth-tables ()
    (interactive)

    ; if-then should be === and
    (if (equal (if-then-truth-table) (and-truth-table))
	(princ "if-then === and")
        (princ "if-then NOT === and")
    )
    (terpri)

    ; if-then-else should be === if-then-else-equiv
    (if (equal (if-then-else-truth-table) (if-then-else-equiv-truth-table))
	(princ "if-then-else === if-then-else-equiv")
	(princ "if-then-else NOT === if-then-else-equiv")
    )
    (terpri)

    ; if-then-else-t should be === implies
    (if (equal (if-then-else-t-truth-table) (implies-truth-table))
	(princ "if-then-else-t === implies")
	(princ "if-then-else-t NOT === implies")
    )

)