Sequent calculus exam question 13.02.2019 Q1. b

Question

Tool proof tree :

I tried solving above question and I got everything correct except the one leaf which is same as mine in tool but in solution it is slightly different.

In the first leaf in the solution it is written as {a,b} |- {} or I1(a) = I1(b) = true but my answer is coming as {b,d} |- {} or I1(d) = I1(b) = true. 

Is there any typo in exam solution ?

Answer 1

Yes, there is a typo in the exam solution. The first variable assignment should be b=d=true instead of a=b=true since the following formula is valid:

((d∨¬(a⊕c))∧b) <-> b & d | a&b&c | !a&b&!c