What does an upside down U mean in math?
Hey there! The upside down U or ∩ means the intersection of two sets. The intersection of two sets means that the elements of one set is common with the elements of another set. Constructing a Venn diagram is always useful for problems like these. The intersection of two sets is represented by the shaded or the overlapped region between the two sets. We know the following are true: Set X = {1,2,3,4,5,6,7,8,9,10} Set Y = {2,3} (note that 1 is not a prime!) Set (X ∩ Y) is set Y or {2,3}, as {2,3} is common in both sets X and Y, Hope it helps!
Prove the following statements if they are true and give a counter-example if they are false.?
The first one is true. You can convince yourself by making a Venn diagram; the two given restrictions make the area inside A but outside B zero, so that A⊆B. As for a proof, go with contradiction on this one. Specifically, suppose that A⊄B. Then ∃ x∈A such that x∉B. Looking at our second condition, since x∈A, x∈AUC, so that x∈BUC as well. But since x∉B, this means x∈C. Now look to the first condition. We now have that x∈A and x∈C, so x∈A∩B. Then we have that x∈B∩C. But x∉B, so this is a contradiction. The second one is false. Actually, (AUB)∩C ⊆ AU(B∩C). I'll leave the counterexample to you, with the advice that you try some discrete sets, like {0, 1, 2}, etc. A Venn diagram might help you decide what exactly you need to find. Feel free to put up additional details or email me if you get stuck.
Give the set-theoretic notation for all positive real numbers that are not multiples of 3.?
It doesn't have to have any axioms( the upside down A, or backwards E) but a logical math definition. -Give the set-theoretic notation for all positive real numbers that are not multiples of 3. -And how far apart would it be to this questions answer? ::Give the set-theoretic notation for all positive irrational numbers.
The graph is a twice differentiable function f is shown in... which one of the following sets of inequalities is satisfied by f...?
The graph is concave down until a point that is (1, f(1)) then concave down after it reaches that point as well. The point is above the x axis and it's basically an upside-down parabola if that makes any sense. I know for sure the f'(1) is smaller than f(1) since f(1) is a horizontal tangent but I don't know how to find the f''(1). Please help! Which one of the following sets of inequalities is satisfied by f and its derivatives at x = 1? 1. f′(1) < f′′(1) < f(1) 2. f(1) < f′(1) < f′′(1) 3. f′(1) < f(1) < f′′(1) 4. f(1) < f′′(1) < f′(1) 5. f′′(1) < f(1) < f′(1) 6. f′′(1) < f′(1) < f(1)
Pre-Calculus - Indicated Set?
I missed the first week of my pre-calculus class due to registration problems, and the bookstore still hasn't processed my textbook order (can you tell I'm having a lot of issues this semester? lol), so I have no idea how to do this. If someone could please explain (preferably in detail) how to answer these problems, that would be fantastic. Find the indicated set if: A = {1,2,3,4,5,6,7} B = {2,4,6,8} C = {7,8,9,10} 1.) A (upside down U) B 2.) A U C 3.) A (upside down U) B (upside down U) C Thanks.