Let A = {1, 2, 3, 5, 6, 10, 15, 30} and define R on A by xRy if and only if x divides y. a. Find any greatest or least element/s. b. Find glb({6, 10, 15}) if it exists.  c. Find lub({2, 3, 6}) if it exists.

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: Let A= {1,2,x,y,z}, and B= {1,2,3,z}. How many distinct elements are in (A*B) intersect (B*A

A: Given that A=1,2,x,y,zB=1,2,3,z To find the number of distinct elements in A×B∩B×A:

Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: 2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and…

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Q: Let U={1,2,3,4,5,6,7,8,9,10}. Let A={1,3,6,8,10}. Let B={2,3,5,7,8}. Determine (A−B)′

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Q: Let a, b, q, r E Z and assume that a and b are not both zero and b and r are not both zero. Show…

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Q: Find the value of a for which V= 8 a 4 is in the set a = 4 -5 0 -8-8-8} 4 -3 H = span

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Q: If A = {2,3} and B = {x|x EZ, x<3}, then A x B = Select one: O a. {(1,2), (1, 3), (2, 2), (2,3)} O…

A: If A=2, 3 and B=x x∈Z+, x&lt;3, then to determine A×B.

Q: Let S = {1,2,3,4, 5}, G = {(1),(123), (132)}. For each element %3D a e S, find stabc(a) and orbg(a)

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Q: 2+13 H.W. Evaluate zdz along the following paths- 1+12 (a) horizontally from 1 + 12 to 2 + 12 then…

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Q: Let a, b € N. Choose all correct statements. O gcd(-a, b) = gcd(a, -b) O ged(2a – b, a + b) =…

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Q: Construct the multiplication table for Zs. Using this table, or otherwise, determine the following x…

A: Solution

Q: Construct the addition table for Zs. Using this table, or otherwise, determine the following x in…

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Q: -275 2. Let A 013 -135 Find the adjoint of A.

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Q: Show that a,b,c are in A.P. If x is the G M be tween a and b and y is the G M between b and c,  then…

A: We have to show if  a, b, c are in A.P.,  x is the G M be tween a and b and y is the G M between b…

Q: Find the greatest common divisor d of 115 and 205 and express d as an integral linear combination of…

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Q: = 9. (15 points). Let S {0, 2, 4, 6, 8} C Z10. Is (S, +10, X10) a subring of Z₁0? Find the identity…

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Q: Let A = {1, 2, 3, 4, 5). Define an operation v by a vb= max {a, b}. Prepare its composition table.…

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Q: Find the value of a for which U = a 1 10 is in the set 0 -1 3 0 H = span 5 3 -1 2 -2 -2 a =

A: The value of a=-7 .Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Determine the wronskian and evaluate for which values a, b, c ∈ R the following equations is…

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Q: Let V be all elements of R2 that have the form (a, a2) where a is a real number. Show that (3,9) is…

A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

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Q: Construct the addition table for Zs. Using this table, or otherwise, determine the following x in…

A: Solution

Q: Let a, m, and n be positive integers with a>1. Prove that am – 1 | an – 1 if and only if m | n. For…

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Q: The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that…

A: Here is the solution

Q: Q2: if A= [{1,2},{3}], H= [{1}, {2,3}], G= [{1,3}, {2}] Show that A, H and G are mutually disjoint

A: Note: " Since you have posted multiple questions. we will solve the first question for you. To get…

Q: Find the value of a for which V= 8 a a 4 is in the set H = span 4 4 -5 0 -3

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Q: mework. Find Sup, Inf, Max, Min of the following subsets of R: S₁ = {2-P +39 +5: p,q,r€ Z+). S₂ = {x…

A: Note: According to Company Guidelines we are providing the answer of only 3 subquestions. Kindly…

Q: - If A = {2,3} and B = {x | x ≤ Z+,x <3}, then A x B= Select one: O a. {(1,2), (1,3), (2, 2), (2,3)}…

A: Given that the setsA=2,3 and B=x | x∈Z+ , x&lt;3

Q: Find the value of a for which v= 8 a -4 -12 is in the set 4 0 -4 -1 0 {6E9 2 -3 5 -3 -4 2 H = Span

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Q: H.w ) find the generated af: ty, 7s7z and Zg

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Q: Let ü = 21 – k and i = i + 3j + k. Compute |ū], |ū], ū × ĩ, and Projzu.

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