8. Let a₁ ≥ a2 ≥ ... ≥ an and b₁,b2,..., bn be two sequences of non-negative real numbers such that for each k, 1 ≤ k ≤n, the inequality b₁b₂bka₁a2 ak holds. Prove that b₁ + b₂ + + bn ≥ a₁ + a₂ + ... tan.

Q: 3.Determine the intersection X ∩ Y. Express the  in interval notation. X = {x/ x>equal 8} and Y =…

A: We have: X=x  x≥8=[8,∞)Y=x  x<7=(-∞,7)

Q: Consider the intervals A= (3,9] and B= [4,12]. What is A∩B ?

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Q: For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this…

A: The main objective is to write an inequality comparing (ln(n))8 and n. The expression ln n is…

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

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Q: 1. Prove the following results using the definition of |- and the triangle inequality. For n N and…

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Q: S is a nonempty set of real numbers that is bounded.

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Q: 4) Let a < b be real numbers. Prove that the half open/half closed interval (a, b) is both an Fo and…

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Q: Let A= {k: k ∈ N, k ≤ 20}, B= {3k−1: k ∈ N}, and C= {2k+1: k ∈ N} 1. A INTERSECTION B INTERSECTION…

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Q: Consider the family of sets F = {Ap}peP, where P denotes the set of prime numbers, and Ap= {p" |…

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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…

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: Consider the following sets: A = {n € Z¹ | n² ≤ 9}, B = {2n | n ≤ Z¹}, C = {2,3,5,8}. For each…

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Q: For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this…

A: Please see the attachment

Q: a) Find P(Z > 1.5) [Select] b) Find P(-1.5 ≤Z≤-0.5) [Select ] c) Find P(Z<-1.5) [Select] ◄►

A: Here Z is standard normal variate  i.e. Z has normal distribution with mean 0 and standard deviation…

Q: (15 pts) List the triples in the relation {(a, b, c) a, b, c are integers such that 0 < a <b<c<6 and…

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Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

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Q: Determine the intersection X ∩ Y. Express the in interval notation. X = {x/ x>equal 8} and Y =…

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Q: II. (Vz € N)(3: € Q)(zz = y) III. 1-1+1-1+..= 0. VI. 7+25 mod 16.

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Q: 2.4. Let A and B be sets of real numbers, let f be a function from R to R, and let P be the set of…

A: As per the policy, we are solving three parts. Please repost it and specify which part is to be…

Q: 5. Let x and y be irrational numbers such that x-y is also irrational. Define sets A and B by A = {x…

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Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

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Q: Q: State whether the following statements are true or false: 1. Let S be a non-empty subset of the…

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Q: VI.[15] Let the Universal set be the set R, of all real numbers. [ Hint: Use real number line to…

A: a). Here A = {x € R |  -3 &lt; x &lt; 0} B = {x € R |  -1 &lt; x &lt; 2} A U B contains all the…

Q: Let  Vi =    x  ℝ    −  1 i  ≤ x ≤  1 i    =    −  1 i…

A: