13. If T is self-adjoint, then S*TS is self adjoint for all S; if S is invertible and S*TS is self-adjoint, then T is self-adjoint

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: 1. Disprove: If A UC=B and AUD=B then C=D. (You may define 2={a,b,c,d,e} for your counterexample.)…

A: As per guidelines we have to solve only one question

Q: 12. Compute M.D 'and its coefficient from the following datá. Classes 7.5- 8.5- 9.5- | 10.5- 11.5-…

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Q: 5. Prove that S(n +1, k+1) = £ $(m, k) (").

A: To prove- Sn+1,k+1=∑m=knS(m,k)nm The falling factorial is defined as the polynomial,…

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Q: If T is self-adjoint, then S*TS is self adjoint for all S; if S is invertible and S*TS is…

A:

Q: 1. For every element x in A, there is an element y in B such that (x, y) E F.

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Q: 7. Let c t- are both even or both odd. Let that o and(t 0, t be permutations in S. Prove t

A: Every permutation can be written as a product of 2 - cycles.Suppose  σ = d1 d2 - - -dsand   ζ = B1…

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Q: Show that for all n, m∈Z if n+m is even, then either n and m are both even or n and m are both odd.

A: Use the results of addition of integers.

Q: Suppose that {$1,...Øn} F p and I F ø; for all i < n. Show that I F þ.

A: Proof: Suppose ϕ∈Γ∗ϕ∈Γ∗. As Γ∗Γ∗ is maximally consistent it clearly follows that there exists a…

Q: ) Show that Sn is generated by ((1,2),(1,2, 3, n)}. [Hint: Show that as r varies, (1.2,3. ny(1,2)…

A: Please check step 2 for solution

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A: The objective is to find Z_2×Z_2.

Q: 22. Find a domain for the quantifiers in 3x3y(xy^ Vz((z=x) v (z = y))) such that this statement is…

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Q: 3. Show that the following refinement is correct (for any g, S, and S,): {-g}; if g then S, else S2…

A: Given refinement is: ~g; if g then S1 else S2. Here ~g implies the negation part of g. That is the…

Q: For allne z, gcdin,nt)=l.

A:

Q: 1. For every element x in A, there is an element y in B such that (x, y)EF

A: Remark: Let A and B be two non-empty sets. A relation R from A into B is subset of A*B. A function f…

Q: 11. Let S= {| -2 }. Show that u= E span S. 1 2

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Q: Let x E Q'. Show that for any n EN, there exists Xn E Q such that |x- Xal <

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A: Let n≥3. Let σ∈Sn such that σγ=γσ for all γ∈Sn. Suppose σ≠i, the identity Then there exists…

Q: 1. Let Z defined by the product of two numbers taken separately from two boxes containing 1, 2,3 and…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 2. Compute the convolution of the following signals for n 20 n n x1(n) = and x2 (n) = (;)" u(n) n…

A: Consider the expression of . Determine the z-transform of .

Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

A:

Q: Let 2=(1,2,3,4,} and C={{1,2,3}, {4}}. Derive the sigma-algebra generated by C, i.e. that smallest…

A: Given set is Ω={1,2,3,4} where C={{1,2,3},{4}} The objective is to derive the sigma algebra…

Q: If E, and E2 are measurable , then (E,UE,) is not measurable . صواب İhi

A: Here we have given E1 and E2 are measurable sets

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

A:

Q: discrete

A: In method of contradiction we start by assuming that given statement is false. Then prove that it is…

Q: Let S = {n + m√2 : n, m ∈ Z}  To prove that the sum of any two elements of S is an element of S.…

A: Given: S=n+m√2:n,m∈Z  (a) Let a+b2∈S for all a,b∈Z and let c+d2∈S for all c,d∈Z Add both these…

Q: 1. Let x, y, z be integers. Prove that if x(y + z) is odd, then x is odd and at least one of y or z…

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Q: 6.4 # 2 Find the matia * ' elative to the basir B' for T A' =

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Q: Answer the following questions about a deli system in a grocery store. Within the system, every…

A: (a) The customer IDs are ranging from p to q  inclusive. and meats with IDs ranging from r to s,…

Q: 19/156) If WG, g) is the Wronskian W(u, v) of u and v in terms of W(f, g). the Wronskian off and g,…

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Q: Prove for all m, n, and k in w, that (m⋅n)k = mk.nk.

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Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

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Q: Let A find on Conditions a,bic and d has infinitely that AX =o many solution . what must there Pere…

A:

Q: Let z = x + yi, z, = 1- 0.5i, and z, + z, = 3-1.5i. Find In(z,) - In(z2) C) In(50) + 2nin A) In(25)…

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Q: 7, SHOW THAT FOR EVERY 2x2 DETERNINAAT ANO CONSTANT K THAT! det (KA) = K²det lA)

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Q: @ 2 show Hhat fox) = e*-x3+2 2+2 is a %3D Permutation on R.

A: In the give question we have to show that the function f(x)=e-x-x3+2 is a permutation on ℝ.…

Q: Prove for a e Z and n e N that gcd(a, a + n) | n.

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Q: Let z = x + yi, z2 = 1– 0.5i , and z, + z2 = 3 – 1.5i. Find In(z,) – In(z2) %3D A) In(25) ± 2niN D)…

A:

Q: 2. Suppose that {v1,... , Vp} is an orthonormal set in R", and that x E R". What can you say about…

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Q: 4) Let m,n, r E Z with m # 0 + n. Show that gcd(m, n) divides r if and only if there exist a, b E Z…

A: Let gcd(m,n) divides r. Then we have to prove that, a·m+b·n=r Since, gcd(m,n) divides r than by…

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A: Introduction: When an argument is given in quantified form, the rules of inference are also used.…

Q: let A to have0 al an must by

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Q: Prove that for all k E N, k ose [coske -sink0j cose Lsinke cosko

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Q: If X(z) = In(z - 2), then what's x(k O a. -ak O b. ak O c. -ak /k O d. others Oe. ak / k O O

A: Given that X(z) = ln(z - 2) We have to find the value of X(k).

Q: Prove that for any k > 0, nk e o(2v™).

A: The complete solutions are given below