(1) In (Z,+) determine ({2, 4,5}), the subgroup gener set {2, 4, 5). (As always, please provide full explana

Q: What is/are the mode(s) of this group of numbers? (4, 6, 9, 5)

A: Mode: Mode is the value, which has the highest frequency among all other values of the observation.

Q: Let U={1,2,3,...,10}, A={1,3,5,7}, B={1,2,3,4}, and C={3,4,6,7,9}. Select A^c∩B^c from the choices…

A: We have solved the given problem using set theory definitions: For any set A, the complement of A =…

Q: Find the order of U_12

A: We have to find

Q: ) Let u=(,2,3/ 니,5147, 위/이, 10 ), A-(,3,5,9), 8-2,5어) Find the Sets B. 2 7 3. 9. 10 2)B' 3) AnB 4) A…

A: A set is a well defined collection of the objects, these objects are called the elements of the…

Q: The cardinality of { Ø, 1, 2, 2, {1, 2}} is

A: We need to find the cardinality of { ϕ, 1,2,2,{1,2}}.

Q: What is the domain of the following {(3, 4), (9, 1), (10, 5), (2, 15), (8, 4)} O {3, 4, 9, 1, 10, 5,…

A:

Q: QUESTION 1 A ta, b), B-(4, 5, 6) List the elements of AxA (4а, 4b, 5a, 5b, ба, бь} a,…

A: Given sets are,

Q: What is the domain of the following {(3,4), (9,1), (10,5), (2, 15), (8,4)} O {3,4, 9, 1, 10, 5, 2,…

A: We have given that { (3, 4), (9, 1), (10, 5), (2, 15), (8, 4)}

Q: Let n, m 2 3. Find the number of 3n-element multi-subsets of the multi-set A = {n.a1, n.ag,..,n.am}…

A: Consider the given information.

Q: Find an orthogonal set with the same span (and same number of elements) as 9 27 12 4 11 21 -10 -91 4…

A:

Q: Consider the power Serics Ž n^ (x-z)^ n=1 Find the radins of conver genue shat is the intrvel of…

A: Consider the series ∑n=1∞nnx−2n We have to find the radius of convergence and interval of the…

Q: How many strings of letters from the set (A, B} have length 11 and have exactly 4 A's (repeated…

A: The Answer is given in step-2.

Q: the set B= {n € Z:(n is odd)^(n > 0)}. %3D

A:

Q: 2. (i) (1 2 3 4 5) (2 5 4 3 1) and (1 5 3 2 4) Find the product of the permutations: (a, az ... Ax)…

A: NOTE- Since the terms in the last bracket of first part are not clear, so solving just second part…

Q: \text { Let } U=\{1,2,3,4,5\} \text { and } A=\{1,2,3\} . \text { Find } A^{\prime} \text { . }

A: Definition used -                          A'=U-A                It is a set of all elements, in the…

Q: Let U= {1, 7, 6, 14, 5, 10, 20, 18) A = {1, 20, 18} C = {7, 6, 14, 5, 10} Find A U C'.

A:

Q: Assume that U= { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, A = { 2, 5, 7, 8 } and B = { 1, 4, 5, 7 }. Find…

A:

Q: Show this collection of subsets a partition of A UBUC {A – (B U C), B – (A U C), C – (A U B), ANBN…

A:

Q: 1) Is {(1, 0,3), (1, 4, -2), (-8, 12, -4), (1, 37, 17)} a linearly independent list?

A: We check given set of vectors is linearly independent or not.

Q: Derive the eauation of the natu Val cu bic TnterPolat ing sPline for the falowlhg (1,!) , (2,1),…

A:

Q: The column to the left represents the answer, to the question that is in the column to the right.…

A: Note:- We have to match answer of left side from their question which is in Right side.

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

A:

Q: Give an example of a closed subset S of R^2 such that conv S is not closed

A: An example of a closed subset S of R2 such that conv S is not closed is given below.

Q: Find an orthogonal set with the same span (and same number of elements) as 11 -9 -7 3 (898) 4 1 3 2…

A: Using Gram-Schmidt orthogonal process:

Q: Are the sets A_4 and A_5 compact sets? Why yes, why not? Ay = (,2] A- [1, 2] u [ 3, +]

A: See the attachment

Q: Consider the set of lattice paths from (0, 0) to (8, 8). You should know one quick formula for the…

A: Using formula,nk=n!n-k! k!i 80=8!8-0! 0!=8!8!=1ii 71=7!7-1! 1!=7×6!6!=7iii 62=6!6-2! 2!=6×5×4!4!…

Q: 2. If P(A)= and P(B) = , can A and B be disjoint? Explain.

A: Given,  P(A)=13  and P(Bc)=14

Q: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: True or False {2,3} is a subset of {-1,2,5,6}

A: Here {3} is not an element of the given set.

Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: Draw the network defined by N = {1, 2, 3, 4, 5, 6} A = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4),…

A:

Q: Let U = {a,b,c,d,e,f,17,18,19,20,21,22}, List the members of the set X'nY', using set braces. X =…

A:

Q: 2) Which sequence of transformations can only be used to pro similarity between two images but not…

A: We know that, Rotation, reflection and translation are rigid transformations. Dilation is not rigid…

Q: By induction Show that S has 2^n subsets

A:

Q: -12 - 기 + 5 30

A: We know |X|=|-X|=X

Q: onsider the 4-lists taken from {1,2,3}. For example, (1,2,1,3).  How many are there in which each…

A:

Q: Let U = 51, 2, 3, 4, 5, 6, 76, A = 51, 3, 5, 76, and B = 53, 4, 66. Find each set. U^{\prime}

A: Given sets - U = 51, 2, 3, 4, 5, 6, 76A = 51, 3, 5, 76B = 53, 4, 66We need to find the prime or…

Q: For questions 1-8, match each set in Column I with the appropriate description in Column II. 1.) (1,…

A:

Q: Find the order of 175 in Z_245

A:

Q: 3.) Nowe consider motrix cif possible) as a linear combination of the motrices in' ls. the set s…

A: Given that: S=3-333,3-245,6-3106To express the the following matrices in the linear combination of…

Q: What is the domain of the following {(3,4), (9,1), (10,5), (2,15), (8, 4)} O {3, 4, 9, 1, 10, 5, 2,…

A: We know that for a pointx,y is domain is x and range is y Similarly, for given…

Q: Let A={-2, 0, 1, 3, 4), B = {1, 2, 3, 4, ...} and C = {−2,0}. Find A. AUB 1-2.0.1.2.3.4.1 (enter an…

A: According to the given information, we haveSet A, B and C are given.