a) What is the support set of X? b) Write out the PMF of X. c) Compute E[X].

Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1 Ą and fh = 1B. Prove…

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Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: Prove that A u (B n C) = (Au B) n (A u C).

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Q: Let T = {x, y}. List all the strings of length 5 over T that have exactly one y.

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Q: Consider the function f : N→ P(N) given by S(x) = {d € N : d|æ}. a) Write out all of the elements of…

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Q: Suppose f : N → N has the rule f(n) = 4n + 1. i) Determine whether f is 1-1. Justify your answer…

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Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

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Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: Let F = [−2, 3) ∪ {−3, π}. Determine max F, inf F,  interior of F, boundary of F,  and closure of F.

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Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

Q: Let R be a reflexive relation on A. Show that R" is reflexive for all positive integers n.

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Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: Let a, b € Z and both nonzero. Prove that gcd(a, b) x lcm(a, b) = |ab|.

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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: く3)-9)12> an 41123

A: we have to find the cross product of the given vectors e and f i.e. e x f. also we have to find the…

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: Let a, b, c. and d be any real numbers such that a < b and c < d. Prove that [a, b] is equivalent to…

A: Answer

Q: Let A = {a, b, c, d, e}, B = {1, 2, 3, 4, 5} and let us consider the function f : A → B, f(a) = 3,…

A: Given that:  f : A → B, f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1.   Since, the images (i.e.…

Q: (1-exjdy of 28 on Find the halutiom

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Q: Gue Functions fandg, FindCa) Cf g) C&) and its dlomiain, and b) (g oF (x) and its. O F(x)--6xtq,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: 7. Show that the function f : R → R* defined by f(x) is not onto. x2 +1

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Q: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z?…

A: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. We observe that  That is the…

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: List the elements of U(18).

A: The elements in  which are relatively prime to are the elements of ..Two integers  and  are called…

Q: rly). Let a) Evaluate r(20)

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Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f…

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Q: Let the set be w = {(a, b )| a, b E R }, investigate whether the associativity holds for the…

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Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

Q: Find the set P([a, b]) x P({0,1)).

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Q: Use Resolution to prove the following theorem schema: A (B C), BEA → B

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…