I am wondering which workbooks can be helpful in solving the following task: For an individual range I = {a,b} show that:
$$ \begin{array}{l}{\text { (a) }\{p(a), \forall X(p(X) \rightarrow q(X))\}=q(a)} \\ {\text { (b) }\{\forall X(p(X) \rightarrow q(X)), \forall X \neg q(X)\}=\forall X \neg p(X)} \\ {\text { (c) }\{p(a), \forall X(p(X) \rightarrow q(X))\} |=\exists X q(X)}\end{array} $$
As I understood, this task is connected to Horn clause, math logic and predicates. But deeping into these topics didn't make me closer to ideas for solving exercise.
May be this answer is not really correct, because file (answer) is in Russian. But finally I found some approaches for solving above mentioned task in this presentation:
http://cloud.bogdan.co/s/D2NCxtZdxbYtBeo
To be sure that this file wouldn't be occasionally deleted, I duplicate it in another cloud:
https://1drv.ms/p/s!As7Xx8xokIvflqhWHZFeQd-8ljzZrg?e=LX7JFL