Q) Let Tright on R ? {(a, o0) : a € R}U {¢, R} . Prove that Tright is toplogy

Q: A AB

A: Is AB is congruent AD what theorem is used to prove this?

Q: -2 4 and w= Let u = -3 -2 For what values of h is wm the plame Spanned by ut and v ? 3=

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Q: [Falkner Section 11 Exercise 26] Let A, B, and C be sets. Prove that if f: A → B and g: B→ C are…

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Q: to,' i.e. Let X be the space of integers and let R be relation 'less than or equal x Ry if x ≤ y…

A: The given relation is .

Q: Theorem 20 (Associative Law). If x, y, z ∈ N, then (x+y)+z = x+(y+z). Proof. (sketch). This follows…

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Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: Find the standart devition. Standart sapmayı bulunuz.     A) 7,39 B) 14,78 C) 54,64 D)…

A: Standard deviation= √(summation fiXi2)/n - {(summation fiXi)/n}^2 n= summation fi = (30+40+60+30+25)…

Q: Question:. Show that R' is a Banach Space.

A: Banach space: A complete normed linear space is called Banach space. Given:

Q: a.) Give e a جا b.) Give

A: We use different techinques for solving this problem. The first one is quite easy and we make use of…

Q: Let Xis Hilbert Sface and T, SEBO), 2 EF then @+*|| = \|TI|

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: (g) i–1 (h) i–2 (i) i -3

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Q: Let u, E C" prove that есп ū. v = v. u

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Q: tor all l sets A, Bad C やok that A xCB-c) = (AX1B J- CAxc). %3D

A: Given below the detailed solution

Q: ∃x ∈ D such that ∀y ∈ E, x + y = 1 Negation:

A: We need to find the negation of  ∃x ∈ D such that ∀y ∈ E, x + y=1

Q: 2 and v = [*] 21. Let u = Show that is in Span {u, v} for all h and k.

A: We have to solve given problem:

Q: 1]If 9:T>V and f:ST and gof IS injective, prove that both f añd 9 are injective.

A: Injective function:- for every x1=x2 implies that f(x1)= f(x2) .or vice versa.

Q: a) Prove that Q R is neither open nor closed. b) Determine aQ.

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Q: 5) Again let Universe U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Let S = {0, 1, 2}, T = {1,4}, R = {2, 4,…

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Q: Let u, v E Z. Show using only the definition of a divisor and algebraic properties that if 7|u and…

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Q: [8 pts] 13) Use the Horizontal line test to determine which of these has an inverse: ギ,长。* a) b) c)…

A: Horizontal line test is use to determine whether the function is inverse or not. If Horizontal line…

Q: If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret…

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Q: Let u (41, U2, Uz). Explain why u•u > 0. When is u•u 0?

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Q: if A = | メ %3D Hint A = B %3D -3 B = %3D 1) find x and y 2) The muti Plicative inverse of matrix B

A: Multiplicative Inverse  The multiplicative inverse of a matrix  is equal to the identity matrix when…

Q: if a2+aEccR; Fos all fiso:e that aER, Ris camutative. then

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Q: Evaluate uv ū + v 29 where u = 1 + 3i and v = −2 — i. 3i

A: Evaluate uv¯u¯+v, where u= 1+ 3i and v= -2-i

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

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Q: If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ,…

A: Given P an Q are represented by the numbers z1 and z2 such that |1z1+1z2|=|1z1-1z2| We need to find…

Q: Homework: Determined whether the following sets are open or closed in (IR", ||. |I): 1) [a , b1] ×…

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Q: Prove that dv du 2 – u? + v² 18

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Q: Show that both R and R2 may be covered by countably many open balls.

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Q: U what the closure of (-a12) in the the rightro

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Q: Assume X = (1,3,5,7}, Y = (1,9,25,49)} and F(x) = x2, such that F:X Y. Then the following is true…

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Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

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Q: Let a, b, c Є Z. Prove that a | b and b c implies a | c.

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Q: Consider the mapping diagram below. a 3 4 a) Write f as a set of ordered pairs. b) Is f 1-1? Justify…

A: (a) f as a order pair is given by {(1, b), (2, c), (3, b), (4, a)}

Q: I R Ris transitive, then 1 is transitive. True False

A:

Q: LetZ:Nlo,1), Find p(IZI>-I |121< 2)

A: Given Z~N0,1