Given:

Q: II. Prove S< M2,2. (Write a detailed, logical, well-organized proof.) s = {[6 1:9r - 7s = 0; r.sER}…

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Q: Suppose that > ak = a and let c E R. Prove, in all the that (c-an) = gory detail necessary, = c•Q.…

A: We will give two proofs one based on partial sums and the other will be a direct proof.

Q: B E D

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Q: Suppose n E N and u, v € V₁ such that |u| = 5, |v|= 4 and u⚫v=-7 Find |3u + v. Find t R such that u…

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Q: 3. Let G = Q3. Find the right cosets of H in G for: a) H = ( K). b) H = (-1).

A: Let G=Q8. We need to find the right cosets of &lt;K&gt; and &lt;-1&gt;.

Q: 3. Given: GH DE Prove: AFGH ~ AFDE F G 工

A: Given data: Line GH|| DE In triangle FGH and triangle FDE m∠F=m∠F  [common angle] We know that line…

Q: Let S denotes the set of real numbers strictly between 0 and 1. Let a and b be real numbers with a <…

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Q: GIVEN: k || l, 5 = x8. PROVE: j || l. 56 3 4 1 2

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Q: Suppose that Pr[A|B] = 1/3, Pr[A] = 1/6, and Pr[B Compliment] = 3/4. Find Pr[B|A Compliment]. (Hint:…

A: Given that, Suppose that P [A|B] = 1/3, P [A] = 1/6, and P [B Compliment] = 3/4.…

Q: Let n E N coprime with p. Show that there exists x, y E Z coprime and such that p | x² + ny² is and…

A: To prove the given claim we have to show that :- x,y ∈ Z ; gcd(x,y)=1 ; p | x2 + ny2   implies…

Q: Prove the given statement by the indicated method. (1). By Direct Proof: "Vm,n € Z*,+> 2."

A: ∀m, n∈ℤ+,We know square of an integer is always non-negative Hence (m-n)2≥0…

Q: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: Let Si = { x ∈ R ∣ x > i } , i=0,1,2,... Are the sets S1, S2, S3 . . .  are mutually disjoint?

A: If two sets A and B are mutually disjoint, then A∩B=ϕ . Define the sets S1 , S2 , S3 as follows.…

Q: . Find the value of to for the following statement to be true: P(- to ≤ t ≤ to) = .99 where df = 30.…

A: Given that, P(-to ≤ t ≤ to) = .99 where df = 30. We have to find the value of to