1. Klenk's Tree Method for Determining the Truth Values of Statements

2. Steps for Computing Truth Values
Place the truth values of the simple sentences immediately above the atomic formulas. (A, B, C, etc.)
Check the statement for any negations attached to atomic formulas (~A, ~B, ~C, etc.) Write the truth value for these negations immediately below them.
Starting with the smallest subformulas and working your way out, determine the truth values of each subformula based on the truth values of its subformulas and the truth table for the major operator of the subformula. Write these truth value below the subformula, connecting it to the atomic formulas with arrows. "Bring down" the truth values for any atomic formulas that remain to be dealt with.
Repeat Step 3 until you have worked your way out to the major operator of the formula as a whole.

3. Example 1 Let A and B be true, and let Z be false T F Step 1
~{[(A  B)  Z] [(B  Z)  ~A]} F T
Step 3a F
Step 2
Step 3b F F
Step 3c
Note: This is the second example on pg. 43 of Klenk, except I've fixed the typo (missing the last set of brackets) so that *now* her explanation makes sense.
Step 3d T
Done!!

4. Example 2 Let A and B be true, and let X, Y and Z be false T F Step 1
({[(A  B)  X]  Z}  Y)  {[(X  Z)  A]  X}
Step 2 (skip) T F
Step 3a
Step 3b F T
Step 3c T F F
Step 3d
Step 3e T
Done!!