Natural Deduction True or False. Place a check mark in the box beside each true statement.

13. True or False? Aa Aa Use your knowledge of natural deduction proofs in propositional logic and your knowledge of the first four rules of implication [modus ponens (MP), modus tollens (MT), pure hypothetical sylogism (HS), and disjunctive syllogism (DS)] to determine which of the following statements are true. Place a check mark in the box beside each true statement. The statement variables (P, q, and r) in the form for pure hypothetical syllogism (HS) may stand for compound statements. The conclusion (indicated by a single slash) indicates what the proof should yield in the end; therefore, you should not cite the condusion line as justification for any lines within the actual proof Modus ponens (MP) requires a conditional on its own line and the antecedent of that conditional on another line. If you have the statement-2 F on one line and the statement-Z on another line, then you can use the modus tollens (MT) rule. In a natural deduction proof, disjunctive syllogism (DS) always requires that you cite exactly two line numbers. You are permitted to cite the conclusion line the line indicated by a single slash as justification for lines within a natural deduction proof If you derive the statement ~R from the statement ~(Zv F) v ~R and from the statement-~(Z v F), then you are using modus ponens (MP). D Modus ponens (MP) requires a conditional on its own line and the negation of the conditional's consequent on another line. The statement variables (p, q, and r) in the form for pure hypothetical syllogism (HS) may stand only for simple statements, not compound statements In a natural deduction proof, pure hypothetical syllogism (HS) always requires that you cite exactly one line number. If you have the statement-Z F on one line and the statement ~Z on another line, then you can use the modus ponens (MP) rule. If you derive the statement ~R from the statement ~(Zv F) v ~R and from the statement ~~(Z v F), then you are using disjunctive syllogism (DS). In a natural deduction proof using the first four implication rules, each new line must follow from the lines above by a rule. If you cannot complete a natural deduction proof for an argument, then the argument must be invalid