By Christos Evangeliou
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Exercise 1-3 1. Can an argument have all true premises and a true conclusion, yet not be deductively valid? 2. Can an inductively strong argument have all true premises and a false conclusion? 3. Can a deductively valid argument have false premises? 4. Can a deductively valid argument have a false conclusion? 5. Can a deductively invalid argument have a true conclusion? 6. Can a deductively valid argument have all true premises and a false conclusion? 7. Can an argument be sound but not valid? 8.
If the statement we substitute for p is true, then its negation is false. 2. If the statement we substitute for p is false, then its negation is true. Again, we can summarize these results with a single sentence: A negation is false if the sentence being negated is true, and true if the sentence being negated is false. 28 Sentential Logic Examples Here are a few of the several ways of expressing a negation. All the following are correctly symbolized as ϳ T (where T ϭ “ tomatoes are vegetables”).
If either or both sentences are false, the conjunction of the two will be false. A great many connectives in English are not truth-functional. ” The sentence “Bill Clinton was president before George W. Bush was president” is true, and the sentence “Bill Clinton was president before Abraham Lincoln was president” is false. Yet for each of these two sentences the component sentences are both true. So the truth-value of a compound sentence formed by connecting two sentences with the word “before” is not a function of the truth-value of the component sentences.
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