Let Ai= {-i, i} for all integers i= 1,2,3,4 find the following a. A1 U A2 U A3 U A4 b. A1 n A2 n A3 n A4

Q: Let i be a positive integer and A, [-i+ 1,1]. Then U14, %3D O R O None of these O F1,11

A: Given that 'i ' be a positive integer and Ai=-i+1,1. We have to find the union ∪i=1∞ Ai.

Q: a. A, = {-i,-i+, ..,-1,0,1, ..., i – 1, i} b. A = {i, i+1,i+2, ...} for every posit c. A, = {0,1}…

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Q: o= (1,8,5,7)(2,4) y=(1,3,2,5,8,4,7,6) a. Compute oy · b. Determine whether oy is odd or even.

A: This question is related to Abstract Algebra (Symmetric Group)

Q: Let i be a positive integer and A, = [-i+1,1]. Then U, A O R O 1-0,1] None of these -1,1]

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Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: What are the values for x1, x2 and x3? O x1-500 ; x2-57.78, x3-175.56 O x1-500; x2=-175.56, x3-57.78…

A: We have given optimization table and we have to find the values of variables that maximize the…

Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

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Q: 3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no…

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Q: Exercise 16: Write up three proofs for the above six theorems. (You should be able to do all of…

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Q: 5. Let a be a real number, c an integer, c > 0. Prove that

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Q: 10. Find U 4, and N4,, where i is a positive integer if (a) A, = {i,i+1,i + 2,.) (b) A, = {0,i} %3D…

A: (a) Given that,  Ai=i, i+1, i+2,..... Then, A1=1, 2, 3,.....A2=2, 3, 4,.....⋮An=n, n+1, n+2,.....⋮…

Q: Let S be any set of non-negative integers with k + 1 elements. Show that there is x, Y E S s.t. k…

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Q: Find U, A; and NË, A; if for every positive integer i, a) A; = {-i, -i + 1, ..., -1, 0, 1, ..., i–…

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Q: Let i be a positive integer and A, = [-i+1,1]. Then U, A= O [-1,1] O None of these O l-00,1[ O…

A: Given that          for i be a positive integer…

Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

Q: 8. Express the following as linear combinations of u = (2, 1, 4), v (1,-1, 3), and w= (3, 2, 5). (a)…

A: (b) ( 6, 11 , 6 )   We have to write it as linear combinations of (2 , 1 ,4 ) , (1, -1, 3 ) and (3…

Q: (a) Evaluate I = SoSi L' dxdydz. (b) In how many possible orders can you calculate I? Do all give…

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Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: 10.

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Q: 8. Express the following as linear combinations of u = (2, 1, 4), v= (1,–1, 3), and w= (3, 2, 5).…

A: The given vectors are:u=2, 1, 4, v=1, -1, 3, w=3, 2, 5

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

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Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1<an, n>N. For n=1 a1=100011! For n=2…

Q: Let i be a positive integer and A, = {[.., i – 6, i – 4, i – 2, i, i + 2,i + 4,1+ 6, . ). Then N 4…

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Q: Let i be a positive integer and A; = {...,i – 6, i – 4, i – 2, i, i + 2, i + 4, i + 6, ... }. Then…

A: Just substitute i equal to 1,2,3,... And you'll observe a pattern.

Q: Let A = a22 Show that if d = a¡|a» – A2jɑ12 # 0, then 1 A- = a22 -a12

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Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: 1. Let A = {m, 2m,3m,...} where meP; that is, Aconsists of the positive integers of m. Find: a) A,…

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

Q: - Show that (for n = 0, 1, 2, ..) (a) F(-n, b; c; 1) = - (c-b)n (c)n

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Let i be a positive integer and A, = {..., i – 6, i - 4, i – 2, i, i + 2, i+ 4, i + 6, ... }. Then…

A: First option is correct

Q: Let i be a positive integer and A = [-i + 1 ,1]. Then UA,

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Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.

Q: Let i be a positive integer and A, = [-i+1,1[. Then N14= %3D

A: We have to find the first intersection first.

Q: Let Af = [i – 1, i] for all integers i = 1,2,3,4. Find the following. a. A1. A2- A3. b. A, U A2 U A3…

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Q: s) Let a and b be positive integers such that b< a < 10b. How many ways are there to place a…

A: In the given problem Balls are labelled and boxes are unlabeled. i.e. we have to distribute a…

Q: 9) Determine whether AMNO = AQRS. Explain. M(0,-1), N(-1,-4), 0(-4,-3), Q(3,-3), R(4,-4), S(3,3)

A: Given, M0,-1;    N-1, 4;    O-4, 3Q3, -3;    R4, -4;   S3, 3 We have to determine whether  ∆MNO…

Q: Prove: Let a, b, c, d be real numbers. If a &lt; b and c &lt; d, then a + c &lt; b + d.

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Q: For any positive integer n and r = 1,2, ...,n, we have G) = (","') + C" - }). True O False

A: The expression nr can be presented in the factorial form as follows. nr=n!(n-r)!r! The expression…

Q: Prove: Let a,b,x and y be integers. If a|x and b|y then (ab)|(2xy).

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Q: Let a1, a2, a3, ..., a11 be positive integers such that (a1)2 + (2a2)2 + (3a3)2 +...+ (11a1u)2 =…

A: Comparing with known series

Q: Let i be a positive integer and A; = [1,i+1[. Then U2, A= O [-1,1] O R O 11, [ O [1, [ None of these

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Q: Let m, n be positive integers. If m n, prove that 5m - 1 5" - 1

A: We show that 5m-1|5n-1 whenever m|n ,for any positive integer m,n

Q: Compute (1+ v3)18 in F17[V3]. Your answer will lie in F17; input it as an integer between O and 16.

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Q: Prove that if a is a positive integer, then 4 does not divide a2 + 5.

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Q: 2. Find U, A, and NE,Ą, where: a. A = {-i, i} for every positive integer i. b. A = {i°, i', i²} for…

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Q: 8. Express the following as linear combinations of u= (2, 1, 4), v= (1,–1, 3), and w (3, 2, 5). (a)…

A: Linear combination :  A vector v∈V(F) is said to be a linear combination of the vectors v1,v2,...,vn…

Q: Let i be a positive integer and A; =[1,i+1[. Then U A;= O [-1,1] O R O 11, [ O [1, [ None of these

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.