Prove that [0,1] has the same cardinal number as [0,2] U[7,9].

Q: Prove that neQ

A: Given ddxxn=nxn-1

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: Show that projv u and u - projv u are orthogonal.

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Q: What is the cardinality of the set of 2 x 2 matrices over N? Prove your answer.  Note: a 2 x 2…

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Q: Prove that AAB = (AU B) - (An B),

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Q: 1. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it…

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Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Find a universe for variable x,y,z in which the statement ƎxƎy∀z((x=z)or (y=z)) is true and another…

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Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: Construct a proof that ZEIF = ZGIH. н

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Q: 3. prove that: det (AB) = det (A) det (B) If a - (;). » - ( :) 2 -1 7 A = 3 2 4

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Q: Let ū (7, – 4, – 2) and i (6, – 1, 4). - - - Compute the following: v x ú = || и хиE 5(ū x i) = йх…

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Q: If a,b,c,d are in continued properties,prove that

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Q: the sets  [0,1] and  [0,1/2)∪(1/2,1] have the same cardinality, give an explicit bijection to show…

A: We will define a bijection from the set J  = [ 0 , 12 ) ∪(12 , 1]   to the set I =0 ,1   First we…

Q: Prove that, there is no simple grcup of order 200.

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Q: Consider the non empty sets A and B such that A and B have the same cardinality. Prove, for any set…

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Q: Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is…

A: It is required to explain the meaning and to prove that the cardinality of power set P(x), of X, is…

Q: Give 3 different examples of norms on Z (set of integers)

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Q: Suppose S and T are infinite sets and d= SoT is a function that is not onto May we conclude that s…

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Q: 6. If u=,%) prove that xu, + yu, + zu, = 0

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Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: 4. Prove that the cardinality of the natural numbers is strictly less that the cardinality of the…

A: "According to Bartleby  guideline, Handwritten solutions are not provided" To prove that the…

Q: 27. Prove in detail that Q(/3+ 7) = Q(/3, v7).

A: We have to prove given equation.

Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: (B) Prove that (Q,|·|) is not complete.

A: A metric space (X,d) is said to be complete iff every Cauchy sequence in X converges to a point in…

Q: Prove that Vtan a de – 7//2.

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Q: 3. Show that Z, -

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Q: Show that gcd(a,n)=1 if these exist m and k such that ma+nk = 1.

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Q: 4. Prove that, VR, -11-

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Q: 5. Verify that if U is open in X and A is closed in X, then U-A is open in X, and A- U is closed in…

A: We have given that , U is open in X. A is closed in X. We need to show that , U - A open in X. Also…

Q: Prove or disprove that U(20) and U(24) are isomorphic.

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Q: Let Az = { k, k + 1, ..., k²}, for k 1,2,3, .. Find U은1Ak-nE1 Ax

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Q: Show that S={(1,0,1), (1,1,0), (1,1,1)} is liearly independent. Give a proof.

A: Vectors in a set are linearly independent if the matrix formed by the vectors as the columns of the…

Q: Give two pairs of things and three pairs of words (3-, 4-, 5-letter words, respectively) that are…

A: Definition and meaning of homeomorphism. A homeomorphism is a mapping which is continuous, one-one,…

Q: Prove that there are compound statements that are not equivalent to any statement using only the…

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Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Prove: 4 x,,x2x, ER, then |x, +x, +.. + x,| s |x,|+|x,|+... + |x,|

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Q: 2 FIND THE PARAMTRIC AND SYMMETRI C EGUATIUNS OF THE LINE THAT PASSES THROUGH (2,8,10) AND く2,8,147…

A: The given data is: The line passes through 2,8,10 and parallels to 2,8,14 To find the parametric and…

Q: Prove that if ACB, then A-B=0.

A: This question can be solved using the concept of set theory.

Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

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Q: if the If the conditions of the existence theorem are fulfilled and the conditions of the conditions…

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Q: Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection…

A: Yes, the sets 0,1 and 0,12∪12,1 have the same cardinality.

Q: Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 0’s.

A: It is given that S = {0,1}.It is known that if n be the positive integer and given a finite set A,…

Q: Please solve part (a).

A: Hi! We are answering only the first two problems. If you need the solution of rest questions, then…

Q: 4. Prove that the sets (–1,5) and [-1,1) U {2} U (3, ∞) have the same cardinality

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Q: -show that. Z, ax Rings.

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Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .

Q: For what values of aand b is {u, v} an orthonormal set?

A: A set of vectors form an orthonormal set if all the vectors in the set are mutually orthogonal and…