Charlie Flowers
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 Sep24 awarded Autobiographer Oct18 accepted Stuck because of possible error in exercise of “How to Prove It” by Velleman Oct18 comment Stuck because of possible error in exercise of “How to Prove It” by Velleman This is exactly what I needed. I went down exactly this path before asking the question. My error was that I calculated $\bigcup_{i \in I} \mathbb(P)(A_i)$ to be {emptyset, 1, 2, 3} instead of {emptyset, {1}, {2}, {3}, {1,2}, {2,3}}. I see now, as your response shows, that the left side of the original problem is a set-of-sets, as is the right side. Thanks. Oct18 comment Stuck because of possible error in exercise of “How to Prove It” by Velleman I am doing something wrong, and I continue to do that same thing wrong no matter which direction I approach it from. It is as if I have identified that the set on the left contains only apples, and the set on the right contains only oranges. If that were true, I would then know that the set on the left couldn't possibly be a subset of the set on the right. And I can't seem to get myself unstuck off that. (I'm sure I'm incorrect in saying that the left is all apples and the right is all oranges, but I haven't yet found my error). Oct18 awarded Commentator Oct18 comment Stuck because of possible error in exercise of “How to Prove It” by Velleman @Tyler, I did that. I used A_1 = {1,2} and A_2 = {2,3}. That led me to $\bigcup_{i \in I} \mathbb{P}(A_i) = \{1, 2, 3\} and \mathbb{P}(\bigcup_{i \in I} A_i) = \{ \{\varnothing}, \{1\}, \{2\}, \{3\}, \{1,2\}, \{1,3\}, \{2,3\},\{1,2,3\} \}$ Oct18 asked Stuck because of possible error in exercise of “How to Prove It” by Velleman Jun10 comment My sister absolutely refuses to learn math What university level books covered topics that were 3 or 4 years below her level as a senior in high school? And more importantly, what university level books would you recommend having around the house for a 10 year old child? What books would you want left around you if you were living your life over again and you were 10? Apr29 awarded Scholar Apr29 accepted How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” Apr28 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” How about if I re-word it as: "If you're inside a 'forall', and you want to make a statement about a subset of the universe, one commonly used way to do so is with an If-Then (aka, 'implication')." Apr27 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” OK, so there are equivalences I don't know about yet that the book will cover soon. That's good. Thanks. Apr26 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” Excellent. Thank you. I was aware of the equivalence you mentioned, and in my mind using it is the same as using an implication. I was wondering if there were other equivalents that don't rely on implication. At this point, I think the answer is yes, but only if you re-word the statement to use existential qualifiers instead of universal qualifiers. Thanks again. Apr26 revised How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” made a better title Apr26 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” Thanks, that is very helpful. Your last example has too many "negations of negations" for me to wrap my mind around. I'll have to spend some time on that tomorrow. But I do like that it presents an alternative with no If-Then, and I see that it had to avoid "forall" in order to do so. So I think this confirms my hypothesis -- I was looking for a guideline to when I'd need an If-Then, and it appears the answer is when I'm inside the scope of a "forall" but I want to make a statement about a subset of the universe. Does that sound right to you? Apr26 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” thanks for your response. I think I have figured out my mistake, and I'd word it like this: "If you're inside a 'forall', and you want to make a statement about a subset of the universe, the only way to do so is with an If-Then (aka, 'implication')." Do you agree? Apr26 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” I think I see a rule. If I'm inside of a "for all" statement, but I actually want to make a statement about a subset of the universe, I'm going to have to use an If-Then. Is that right? Apr26 awarded Editor Apr26 revised How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” added a third potentially equivalent logical statement Apr26 comment How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.” OK, thanks. So I think you're telling me that my problem is I'm including in the "conversation" people who are not even in the Discrete Math class, where I was supposed to exclude them. Is that right? And if so, can you see a way to exclude them without using an If-Then?