Q.3 Explain operations on classical / crisp sets
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A: vectors span R3 means that some combination of the vectors can take up all of the space in R3.
Q: (2) Is the set {r € Rr² € N} countable? Justify your answer.
A: Yes the set A={x €R : x2 €N } is countable
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Q: F (8)
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Q: 7. (12 points) Use a proof by contradiction to prove: For all sets A, B, and C (A\C)n(B\C)n(A\B) = 0
A: Step 1: proof let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…
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A: Please see the below picture for detailed solution.
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- please send correct answer Q122. Rewrite the following sets using list lotation. (Like A = {1,3,5}.) (a) A = {r| x is odd and 01. Let A = {−30, -10, 10, 30, 50} and B = {-20, -10,0, 10} be subsets of the universal set ε = {10x: x = Z and -3≤x<6}. (a) List the elements of An B and (AUB)'. (b) Evaluate: (i) |AB|; (ii) |A × B|; (iii) |P(A)|; (iv) |P(B) = P(A)|. [1] [2]Question 1. 1. Use the operations in o-algebra, such as union, intersection, difference, countable union and countable intersection to generate the following intervals from intervals of the form (a,0), where a ER. a) [a, ∞) b) (-∞, a) c) (-∞, a] d) [a, b] 2. Use the fact that the interval (a, ∞) is measurable for all a € R to justify the measurabliity of intervals in (1).2. (Sets) Given the universal set U = {n €N|1sns 10}, and the sets A = {n €U|n is the square of an integer)}. B= {n €U | n is even or prime),. please (a) List all elements of A. (b) List all elements of B. (c) Let E be the set containing all even numbers (in U), and P be the set containing all prime numbers (in U). Write B in terms of E and P, using unions, intersections, and complements (if necessary). (d) Verify the statement (An B) = AUB. (List all elements of all relevant sets.)Your answer MUST have a RIGOROUS proof (not just explanation, some math that THOROUGHLY demonstrates ALL cases work) AND Farey Sequences1. For given fuzzy number A={(3/0,4):(4/0,6)(3/0,8)(4/1)}; B = {(2/0,7):(3/1):(4/0,7)}. Determine A+B, A-B, A B, A/B. 3. Write analytically fuzzy L-R numbers A and B show them graphically. Find A+B, A-B, A-B, A/B, A. Results presents as L-R number, analytically and analytically. A= (3,2,3), B= (4,3,4), L=f, R=f. 1-|x], if -1Let A = {31, 33, 35, 37, 39}, which of these is a correct set builder notation for A? There may be more than one correct answer. OA. (2x +1: x € Z and 15 < x < 19} OB. {x :x is odd and 30(Q x {-T, 1})U{-3n, –2n}UZ is an empty set an uncountable set a countable setWhich of the following sets spans R3? None of these O {(0,1,-1)} O {(0,1,-1),(0,0,0)} O {(-3,0,2).(5,1,0),(0,1,-1)}answer asap the correct option1) Finite Cardinalities A. For any two sets, is this statement true: n(AUB)=n(A)+n(B) - n(ANB) B. For any two sets, is this statement true: n(AUB)=n(A)+n(B)? Explain. C. Is it possible for n(ANB)=0? Explain. D. Is it possible that n(AUB)=0 and n(ANB)=3? Explain. E. Is it possible that n(AUB)=3 and n(ANB)=0? Explain. stions:SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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