[For the following exercises, Ive abbreviated strings of quantifiers of the same type such as xyz simply as xyz.]

1. Use fully developed open branches of trees to construct interpretations (models) showing that the following sequents are incorrect.

a. xFxa, xGax |= x(Fxa & Gax)

c. xyFxy |= xFxx

e. x(Fx & yGxy), xy(Gxy Hx) |= x(Fx Hx)

g. x(yFxy yGxy), x(Hx yFxy) |= x(Hx yGxy)