The key to working a LogicCoach truth tree is understanding the function of the ? in the tree.  When the tree opens, it looks like:

The first step is to edit the line (K⊃~M)•(M≡~K) by either clicking on it once and then pressing Edit or by double clicking on it.  This action will open up the branch editor in which you will lay out how the tree should be built to represent this lines components, or how to deconstruct this line.

The left most column shows the LogicCoach suggestions for how to build the tree.  By clicking in one of the branch columns, you decide which to use and where to use them.

Since the tree for the • continues in the same branch, that is where to place its components.  Before pressing Ok, the editor looks like:

Since (K⊃~M)•(M≡~K) is directly above the ? in the tree, pressing Ok in the editor builds the tree according to your instructions.  The result is:

If you right click on (K⊃~M)•(M≡~K), you will mark it as already checked.  (In the text, the √ is shown to the right of the line, in LogicCoach to the left so that it is always visible.)

Now, you have to decide whether to continue building the tree next for K⊃~M or for M≡~K.  Suppose we start with K⊃~M.  Again, either click on it once and then press Edit or double click on it.  Now the decomposition editor looks like:

After you show how to continue the tree, the editor looks like:

Now when you press Ok, you are returned to the tree but nothing seems to have changed.

This is where you need to understand the ? and what it does.  Double clicking on it, builds the tree at that point according to the instructions that you Okayed in the deconstruction editor!

Each column of the LogicCoach tree ends with a symbol that indicates the status of the column above it.  The ? indicates that the column is not finished.  The ↔ indicates that the column has branched, formed an inverted Y.  (Note that each column is either numbered or is labeled as the trunk.  These column indicators prove very helpful if the tree becomes wider than your computer screen.)  Again, you can check off the K⊃~M, or you can just go on without adding this reminder.  Suppose we just turn to the M≡~K line.

When we return to the tree, there are two ? where the new lines need to be inserted.

Note the use of the left and right pointing arrows to indicate how the tree is growing.  But the real focus should be on the ? since we are done building the tree.  Now we need to judge the branches.  By right clicking on the ? (or pressing the Delete key) the ? can in turn be cycled through X, open, and ? again.

Leave it X if the branch closes (contains a pair of propositions of the form p and ~p) and open if it does not close.

Finally, double clicking on a column ending label will result in a √ if it is correct and an error message if it is incorrect.

Note that you only have to check as many columns as are necessary to judge the entire tree.  For exercise T1, this occurs once at least one open and at least one X (closed) branch is found.

Now you can check the exercise, the entire tree.