You are asked to compute a counterexample for a formula. b&!a is just an example of such a counterexample.
For example, I(b)=true (a)=false is a counterexample, then submit b&!a as your solution.
So you generate the proof tree for the formula your are given, read a counter example of your choice. You will get a partial assignment that assigns some variables to true some to false. Variables assigned to false get negated, the other ones are used as bare variables. You then just build the conjunction of these variables, and that's your solution for the teaching tool.
