Use logical reasoning to prove the following statements. Note that you can only use the rules...

  

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Use logical reasoning to prove the following statements. Note that you can only use the rules in Table 3.2.1 in chapter 3 in the book, DeMorgan's law, contrapositive rule that has this format:: a) b) A → B BA and a new rule that's called Conditional Simplification that has this format: A BAC A B (Note that both rules can be proved by laws of propositional logic.) q→ (p^r) 8 T 9 7778 pu US 149 pq Table 3.2.1: Rules of inference known to be valid arguments. Rule of inference p p-q : q -q p-q :-P Р pvq рла P Р UA q :.p^q p-q 9-r :per pvq q Name Modus ponens Modus tollens Addition Simplification Conjunction Hypothetical syllogism Disjunctive syllogism Use logical reasoning to prove the following statements. Note that you can only use the rules in Table 3.2.1 in chapter 3 in the book, DeMorgan's law, contrapositive rule that has this format:: a) b) A → B BA and a new rule that's called Conditional Simplification that has this format: A BAC A B (Note that both rules can be proved by laws of propositional logic.) q→ (p^r) 8 T 9 7778 pu US 149 pq Table 3.2.1: Rules of inference known to be valid arguments. Rule of inference p p-q : q -q p-q :-P Р pvq рла P Р UA q :.p^q p-q 9-r :per pvq q Name Modus ponens Modus tollens Addition Simplification Conjunction Hypothetical syllogism Disjunctive syllogism