Introduction to Logic. Exercises: Categorical Propositions Answers. 1 The Square of Opposition. Directions: Assume that the given proposition is true, perform the required logical operation, and state the resultant proposition. Then state the resultant truth value. Example: What is the contradictory of ”No mass cults are art.

Concerning exercise C from chapter 14, It seems to me that the argument 10. From previous exercise can also be considered as problematic when translated using “if then ” for the reasons explored in chapter 15, as it has “not-P or Q” among its premisses, and the conclusion is in the form “if P then Q”. Consider: Either Wordsworth didn’t write “The Lord of the Rings”, or he wasn’t a novelist. It isn’t the case that Wordsworth wasn’t a novelist and that he wrote at least one novel.

So, if Wordsworth wrote “Lord of the Rings”, he wrote no novels. Here, it seems that if the first premiss is endorsed on the basis that Not-P is asserted, the material conditional in the conclusion won’t be robust. I had the same problem with this answer, and it seems wrong. Indeed, it seems to contradict the explanation given in the book for (v) “If C is a contradiction, and A1, A2,, An, B tautologically entail C, then A1, A2,, An, tautologically entail ¬B.” (p. There it is clearly stated that “if C is a contradiction, C is never true on any valuation.” But then in the answer to exercise 13 C6, Smith says “if A is a contradiction, then there is no valuation which makes A false.” Something is not right here. Summer Days English Patch there.