TABLE I Rules of Inference.8. Define and label the propositions in thehypothesis with logic variables (p,q.r,...), thenconstruct the logic argument using conjunction,disjunction, implication, bi-conditional, andnegation. Finally, list the Rule(s) of Inferencethat apply in order to validate this argument.Rule of InferenceTantolngyName[PA(p- -Modus ponensModus tollensI eat a balanced diet and exercise daily.If 1 do not get 8 hours of sleep then I do notexercise daily. Therefore, I get 8 hours ofsleep.Hypothetical syllogismDisjunctive syllogismanswer:P- (pV4)AdditionSimplification[(p) A (g) - (png)Conjunction.. pAg[p vq)^(-pvr)] - (a vr)Resolution

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Description: TABLE I Rules of Inference.8. Define and label the propositions in thehypothesis with logic variables (p,q.r,...), thenconstruct the logic argument using conjunction,disjunction, implication, bi-conditional, andnegation. Finally, list the Rule(s) of

Let p denotes the statement p:I eat balanced diet q: I exercise daily r: I get 8 hours of sleep Hence, given argument can be written as p∧q, ¬r→¬q, ∴rwe have to check the validity of the given argument using rules of inference we make the following table: No. Step Reason 1 p∧q Premise 2 q simplification of 1 3 ¬r→¬q Premise 4 ¬¬r modus tollens on 2 and 3 5 r double negation law on 4 Thus, we reach to conclusion r. Hence, given argument is valid.

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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

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

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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TABLE I Rules 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
Tantolngy
Name
[PA(p- -
Modus ponens
Modus tollens
I eat a balanced diet and exercise daily.
If 1 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:
P- (pV4)
Addition
Simplification
[(p) A (g) - (png)
Conjunction
.. pAg
[p vq)^(-pvr)] - (a vr)
Resolution

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