5. Let A = {1, 2, 3, 5, 6, 10, 15, 30) and define R on A by Ry if and only if a divides y. a. Show that (A, R) is a poset. b. Draw the Hasse diagram of the poset. c. Find any maximal and minimal element/s. d. Find any greatest or least element/s. e. Find glb({6, 10, 15}) if it exists. f. Find lub({2, 3, 6)) if it exists. (

Q: Use the given sets to find A∩B A={2,3,5,8,11,15,20} B={4,6,7,9,10,12,13}

A: NOTE: Refresh your page if you can't see any equations. . given sets are

Q: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

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Q: Use the cofactor expansion to compute the following determinant: 7 7 8 det -1 -10 -10 = 0 8 -2 -10

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Q: Answer the following questions for the poset ({{1}, {2}, {4}, {1, 2}, {1, 4), (2, 4), (3, 4), (1, 3,…

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Q: Does {(1,2), (–2, –4), (3, 6)} span R??

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Q: Let a = and a = The set (a, a, ) will span R unless h = (If there are no values of h that make the…

A: For an n-dimensional vector space any set of n linearly independent vectors will span the vector…

Q: Suppose that A and B are subsets of S. Express symmetric difference of A and B (AtriangleB) in terms…

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Q: Direction: Define subsets of Za, as follows: A = {a | a E Za and a 5} A = {a | a E Za and 3| a} 1.…

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Q: Let A:= {2} and B:= {2,3,5}. Give the Cartesian product of sets A and B, furthermore the power set P…

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Q: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

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Q: Logarithmic potential Consider the potential function 9(x, y, z) = In 1 (x² + y? + z?) = In |r|,…

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Q: Let AAB denote the symmetric difference of the setsA,B. Suppose that A = {1,2,3,4} and B= {2,4,6,8}.…

A: Symmetric difference means elements which are in either of the sets but not both.  Thus, symmetric…

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: The given matrix is: A=-300010-180-2 Reduce the matrix to identity matrix form by performing…

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

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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: Find a formula in terms of k for the following determinant - -3-4-6 det -1 8-9-0 k -1 3

A: We have to find a formula in terms of k for the following determinant:

Q: Let a, b e N. Choose all correct statements. O gcd(a, b) = gcd(-a, -b) O gcd(a, b) = gcd(a², b²) O…

A: We apply property of GCD to solve the problem

Q: For the poset, R = ( { 1, 2, 3, 5, 10, 15, 20, 25, 30, 35, 50, 70 }, | ):   Draw the Hasse digrams…

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Q: Let K = {A, Ā, A-°, A-o-, A°, A°¯, A°-o}. Show that K is closed under the interior and closure…

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Q: 2. Let f and g be permutations. Show that the fgf¯ is the same as the order of g. order of h =

A: our objective is to prove the result

Q: raw the Hasse di

A: Given, the poset x is a divisor of on the set                           {1, 2, 3, 5, 6, 10, 15, 30}…

Q: 5. Show the span {(1,0, 1), (–1,2,3), (0, 1, – 1)} is all of R³. 6. Determine whether span {(1,…

A: (5) The given set is 1,0,1,-1,2,3,0,1,-1. The main objective is to show that the span of the given…

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: Find a unit vector with the same direction as the given vector . Use the square root symbol where…

A: v→=81 To find the unit vector in the direction of v→.  Formula: v^=v→v→

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove <-…

Q: 1. Use set identities to show that (A U B) n (B U A) = A where A and B are sets. Let A = {1,2, 3}…

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Q: Let A = {1,2,3} and B = {1,2,3, 4}. The relations R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2),…

A: Given that  R1={(1,1),(2,2),(3,3)}R2={(1,1),(1,2),(1,3),(1,4)} We need to find  a. R1∪R2b. R1∩R2c.…

Q: Let A = {0, 1, 2} and let B = {-2, 0, 1, 2}. %3D

A: Given,        A=0, 1, 2, and B=-2, 0, 1, 2

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

A:

Q: If the set A has 3 elements and the set B = {3, 4, 5}, then find the number ofelements in (A×B).

A: Given that n(A)=3 From B = {3, 4, 5} we see that n(B)=3