TABLE I Rukes of Inference. 8. Define and label the propositions in the hypothesis with logic variables (p,q.r,..), then construct the logic argument using conjunction, disjunction, implication, bi-conditional, and negation. Finally, list the Rule(s) of Inference that apply in order to validate this argument. Rule of Inference Tantulogy Name Modus penens Modus tellens I eat a balanced diet and exercise daily. If I do not get 8 hours of sleep then I do not exercise daily. Therefore, I get 8 hours of sleep. Hypothetical syllogism Disjunctive syllogism answer: Addition Simplification Conjunction

If I study hard, I will graduate with flying colors. If I graduate with flying colors, I will be employed in a good company. If I will be employed in a good company, I will get rich. | am poor. I will study hard, or I will get married. Therefore, I will get married. In proving this argument, what rule of inference is used below: If I study hard, I will be employed in a good company. If I will be employed in a good company, I will get rich. Therefore, If I study hard, I will get rich. A Modus Tollens В Addition C) Hypothetical Syllogism D Disjunctive Syllogism

D part only plz. Thankyou.

Hello. Please answer the attached Discrete Mathematics question correctly and follow all directions. *If you answer correctly I will provide a thumbs up for you. Thank you.

Use the rules of inference and the laws of propositional logic to prove that each argument is valid. Number each line of your argument and label each line of your proof "Hypothesis" or with the name of the rule of inference used at that line. If a rule of inference is used, then include the numbers of the previous lines to which the rule is applied. 비 (c) (d) D EXERCISE 1.12.2: Proving arguments are valid using rules of inference. → P→ (q^r) -q -P (p^q) →r -r 9 :-P (pvq) →r p Ar pvq -pvr -q p→q r-u par q^u Feedback?