(Single Sided) Trees We are not going to cover the double sided tree method given in Chapter 11. In my opinion, double sided trees are harder to learn.

Or Follow this link (Single Sided) Trees We are not going to cover the double sided tree method given in Chapter 11. Instead, I will cover Single Sided Trees. They are summarized in Appendix 4 (p. 233) and explained in your course packet in the section called “How to Make a Tree” Or Follow this link

(Single Sided) Trees We are not going to cover the double sided tree method given in Chapter 11. In my opinion it is harder to learn. Instead, I will cover Single Sided Trees. They are summarized in Appendix 4 (p. 233) and explained in your course packet in the section called “How to Make a Tree” Further information is given at www.miami.edu/phi/one-sided-trees or on your Prop Logic CD in the file: ch11a.txt

The truth table method can be very inefficient. (Single Sided) Trees The truth table method can be very inefficient.

The truth table method can be very inefficient. (Single Sided) Trees The truth table method can be very inefficient. Number of variables Number of rows in the table 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024 Exponential Growth!

the premises are (all) T The Basic Idea Counterexample A row of a table where the premises are (all) T and the conclusion is F.

the premises are (all) T The Basic Idea Counterexample A row of a table where the premises are (all) T and the conclusion is F. P T F T F QT T F F Q>-P | P>Q T F T F T T T Counterexample

The Basic Idea Counterexample Counterexample A row of a table where the premises are (all) T and the conclusion is F. P T F T F QT T F F Q>-P | P>Q T F T F T T T Counterexample If we had known to calculate row 3, we would have needed to do only ¼ of the work.

For more click here The Basic Idea Counterexample Counterexample A row of a table where the premises are (all) T and the conclusion is F. P T F T F QT T F F Q>-P | P>Q T F T F T T T Counterexample The tree method helps us find counterexamples quickly and efficiently. For more click here