Find the cardinality for each of the following sets. > 10 D {0, 1, 5} x {1, 3} { x = Z x² < 8} Z+ - Q {({0}, 0), (0, {0})} P({0}) {{0}, 0, {{0}}} 1. 1 2. 2 3. 3 4. 4 5. 5 6. 6 7. 7 8. 0

Q: .If X&Y are independent R.V's,what are the values of Var(X₁+X₂)and Var(X₁-X₂)

A: Solution X1 and X2 are independent random variables then Cov(X1,X2)= Then Var(X1+X2)=Var(X1)+Var(X2)

Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

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Q: Which of the following sets spans Rº 3 None O {(1,2,3),(0,0,0)(-2,1,0)} {(2, – 1,2),(4,1,3),(2,2,1)}…

A: vectors span R3 means that some combination of the vectors can take up all of the space in R3.

Q: Find the following cardinalities (Do not list the elements of the sets). A² = A x A, for any set A.)…

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: Q14D. Define the sets A, B, C, and D as follows: A = {-3, 1, 6, 7, 10} B = {-10, -5, 1, 4, 6} C =…

A: Given:A=-3,1,6,7,10B=-10,-5,1,4,6C=x∈Z : x is oddD=x∈Z : x is positive To find: A∩D Also, express…

Q: If R = {1, 4, 6, 7) and T = {4, 7, 9), find the following sets. (A) {x| XER or xET) (B) RUT (A)…

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Q: Which of the following sets spans R? O {(3,0,-2)} O (3,0,-2),(0,0,0)} O ((3,0,-2).(5,1,0).(0,-1,1)}…

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Q: 1. Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. a) Find the domain of f: {1, 2, 3, 4, 5} O {2, 4, 6, 9}…

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Q: Q14D. Define the sets A, B, C, and D as follows: A = {-3, 1, 6, 7, 10} B = {-10, -5, 1, 4, 6} C = {x…

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Q: Let A = {x € Rx > 5 and x 15 and x 8 and x < 12

A: Given:- A=x∈R|x≥5 and x&lt;18 B=x∈R|x≥15 and x≤22 C=x∈R|x&gt;8 and x&lt;12

Q: Let X-bin(12,0.4), then P(5 <= X < 10) is closest to: a. 0.334 b. 0.562 c. 0.332 d. 0.335 e. 0.559

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Q: Question 3. Show that the following pairs of sets have the same cardinality. (1) Integers divisible…

A: Advance maths

Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: Complement: The complement of a set A is the set of elements in the universal set U that are not in…

Q: 3. Use function f(x) = *** to show that Card(R – {5}) = Card(R – {1}) step by step. (Note: Card(A)…

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: The sets A, B, C and D are defined as follows: A = {-1, 0, 1, 2, 3} B = {1/2, 1, 4} C = {x | 0 &lt;…

A: The sets A, B, C and D are defined as follows: A = {-1, 0, 1, 2, 3} B = {1/2, 1, 4} C = {x | 0 &lt;…

Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

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Q: upper bound, just write "none." а. (2,3) b. (2,3] С. О

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Determine the values of the following set expressions. {0} × {0, {0}} 0 ×{{0}} P({{0}}) P({0, {0}})…

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Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: Which of the following sets are equal?A = { 0 , 1 , 2 } B = { x ∈ R | − 1 ≤ x &lt; 3 } C = { x ∈ R |…

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Q: Q15A. Define the sets A, B, C, and D as follows: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C…

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Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

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Q: 1. Find the GLB of the set: {x:|x - 4| < 1}. -1 b. 1 -3 d. 3 e. 0 а. с.

A: We need to solve the given inequality to find GLB

Q: {e, 9) € R² : 52. {(x,y) € R² : (y-x)(y+x) = 0} (y-x²)(y+x²) = 0}

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Q: If X, Y are finite sets with |X|=4>2= |Y. How many surjective functions f: X→ Y are there? 2 16 8 O…

A: Let us solve above problem

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Let v = (5, 1, 2) and w = (4, –3, 6). Find each of the following: v+ w, v– 3w, || v||, || v – w ||

A: Solution: The objective is to find the required values

Q: 2. Express the set using the roster method. (x | XEN and xs 5) Choose the correct answer below. O A.…

A: In given question, we can define the set using roaster method.

Q: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C = {yEZ: y ≤ 10 and y is even}. D = {y EZ: y ≤ 7…

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Q: 6. (a) Let sets S = {A, B} × {1, 2, 3} and T = {A, B} × {1, 2, 3, 4} . How many different one %3| to…

A: The total number of elment in set s will be  and total number of element in set T will be

Q: For each of the following sets, tell if it an infinite set, finite set or an empty set. v 1. {x E R:…

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Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

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Q: (Q × {-T, 1})U{-3n, –27}UZ is O an empty set O an uncountable set O a countable set

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Q: Which of the following sets are equal? A = {b, g, j} B= {x, y} C= j, g, b} D= {x|1sx<3 and xEN} J=…

A: Here, A = {b, g, j} B = {x, y} C = {b, g, j} D = {1, 2, 3} J = {0, 2, 4, 6, .....} K = {6, 8, 10,…

Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

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