Consider the following inference rules for reasoning with conjunction and True. These rules are formulated using an approach to proof systems for logical valid- ity known as natural deduction (see the book by Troelstra and Schwichtenberg for much more on this topic [39]). :true-intro True =F ^ F =A and-elim 1 1. Some very basic questions: =F =F ^ F =F ^ F = F FFAF FFAF =F FAF F What is the form of judgment for these rules? What are the premises of the and-intro rule? What is the conclusion of the and-intro rule? Which rule is an axiom? 2. Give a derivation of True A (True A True). 3. Show that the following inference rule is derivable: and-intro and-elim2 = False False A False and-commute 4. Which of the following rules is admissible in this proof system (more than one might be)? True True A F