2. Formal methods play essential roles in education and training of software engineering. Besides the fact that formal methods themselves can be direct solutions to problems in development, many insights into modelling, specification, verification and validation can be provided. a) How can you prove that the set of natural deduction rules with respect to the truth-table semantics given with the use induction on the structure of proof trees? Let X be the set of well- formed proofs. b) Then X is an inductively defined set; the set of rules of the proof system are the rules for constructing new elements of X from old. Let P(x) be the statement ''if x is a valid proof tree ending with o1... onHy then ol... onky". Show and demonstrate how we can prove Vxe X, P(x) by structural induction, and you have to consider each inference rule; for the rules with subgoals above the line so that your answer can inductively assume entailment. 2. Formal methods play essential roles in education and training of software engineering. Besides the fact that formal methods themselves can be direct solutions to problems in development, many insights into modelling, specification, verification and validation can be provided. a) How can you prove that the set of natural deduction rules with respect to the truth-table semantics given with the use induction on the structure of proof trees? Let X be the set of well- formed proofs. b) Then X is an inductively defined set; the set of rules of the proof system are the rules for constructing new elements of X from old. Let P(x) be the statement ''if x is a valid proof tree ending with o1... onHy then ol... onky". Show and demonstrate how we can prove Vxe X, P(x) by structural induction, and you have to consider each inference rule; for the rules with subgoals above the line so that your answer can inductively assume entailment