Given an ordered integral domain ≺D,+,⋅≻, then D has characteristic 0, by the following line of reasoning : e∈Dp⟹ne∈Dp for each n∈N. Thus ne=0D for some n, since a positive element cannot be 0D. Therefore the characteristic cannot be n≠0.   True False

Q: Prove that if alb and alc then a (bx + cy) for all integers x, y.

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Q: 4. (а) Let a, b, c E Z. Prove that, if a | b, then ac | bc, but that the converse may be false. (b)…

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Q: Suppose X and Y have joint characteristic function (s, t). Show that, subject to the appropriate…

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Q: Show that For all z E C, with z # 0, then: |z/²z=1 = z

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Q: . Let A, B = M₁ (F) where n is odd and the characteristic of F is not equal to two. Prove that if AB…

A: AB = -BA.  Take determinant on both sides, we get  det(AB) = det(-BA) = (-1)^n det(BA) = - det(BA) ,…

Q: ZW and ZX are supplementary and ZW and ZY are supplementary. Construct a proof that ZX = ZY.

A: <W  and < X  are supplementary angle  the sum of supplementary angles = 180 degree <W  and…

Q: 5. Prove the following identity for n 2 1: Fzn+1 = F+1+ F;

A: We need to prove that ,  F2n + 1 = F2n+1 + F2n We know that ,   Fm+n = FmFn+1 + Fm-1Fn ,  m ≥ 1 , n…

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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Q: Let α belong to Sn. Prove that |α| divides n!

A: The symmetric group ​ is the group of permutations on n objects. Its order is .

Q: all your calculations and simplify your answer completely. Il you only give a final an- Swer you…

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Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

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Q: If P(A/B) = 0, then A &B are: Select one: a. Mutually exclusive b. ACB с. ВС А d. Independent

A: There are two events A and B such that PA|B=0 PA|B=PA∩BPB=0 Therefore it follows that PA∩B=0

Q: Prove that R(5, 5) < 50.

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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: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

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Q: (9) Prove that for integers x, y and z, if x² + y² = z² then either x or y is even.

A: We use method of contradiction to prove given statement.

Q: Is 1z = 1 for all z ∈ C?

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Q: cov (A)=0 2. Show that co

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Q: ). Find 1 |z-j|=2 Z

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Q: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

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A: for net price  equivalent rate determine first find the complement of the chain discount rate…

Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

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