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

Q: For all integers a, b, and c, if a/b and a|c, then a|(5b – 7c). -

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Q: Prove that Vn e N (the set of natural numbers), ÷+ ɛ N. 3 +

A: We have to use proper manipulation.

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: Let H = {0, +-4, +-8, +-12,....}. How many distinct left cosets of H in Z are there? Explain your…

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Q: left cosets

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Q: Let R = [1, 2] × [1, 2]. Compute ye*"dA. R

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Q: Let a be an algebraic integer in Q(v-37) and let A = (2, 1 + v-37). Prove that either a or a –- 1 is…

A: Given that,         α is an integer in Q-37 lets consider  α=-37⇒α-1=-37-1

Q: Prove that there exists two integers a and b such that a+b > ab

A: We want to prove that there exists two integers a and b such that a+b>ab

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

A: Here f and g are tow permutations  and we are given that h=fgf-1. We have to show that both f and g…

Q: Let A be the subset of the real numbers given by A = {1 + a : a ∈ R and a > 0}. Show that inf A =…

A: A={1+a:a∈R and a>0}Now,1+a>1 for all a∈R and a>0Thus 1 is a lower bound of A.We shall show…

Q: Let 1 3 5 -8 5 -5 1 -1 -3 1 -2 -5 4 -9 9 -2 -2 9 7 Enter the singular values of A in decreasing…

A: Given matrix: A=15-5143-1-31-25-54-99-8-2-297 To find: The singular values of the matrix in…

Q: 3. Prove that if m is a positive integer and x is a real number, then 1 2 m 1 [mx] = [x] + \x + = |…

A: The greatest integer function is one of the most important real valued number theoretic function.…

Statements and Logic

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