2. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Y = {y|y= 2x, x € Z} Enumerate: a.) X - Z b.) Xu (YnZ) X = {1, 3, 5, 6, 7} Z = {z | z is a prime number} c.) Z - Y - X d.) YU (X - Z)

Q: 1- sketch the set of points determined by the given condition: (a) z-4+1=3 (b) 17-11 2+4 |

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

Q: b let fl) = an+b and g) = Cn+d where a,b;c and d Constant. Detemine for which constant a,b;c and d…

A: The objective is to find the constants a, b, c and d such that fog=gof where fx=ax+b and gx=cx+d

Q: 26) If x, y, u, v are variables connected by the relations 1 1 x? =au? +bv2, y² =au² –bv² where a…

A: Given, x2=au12+bv12…1y2=au12-bv12…2 Equation 1+2 gives:…

Q: 9. Let u = : (4, -1), v = (0, 5), and w = (-3, -3). Find the com- ponents of a. u + w c. 2(u - 5w)…

A: We have u=(4,-1)v=(0,5)w=(-3,-3)

Q: Q. One of the following statements is wrong: a.-1,0 = 1.100/ 6.(2,3=| 2.5) C. (1. 2) = R d.(2,3) =…

A:

Q: Ax) = 2& + 2) -2 -1 1 2 y

A: Given, Exponential function f(x)=2(x+2)

Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

A:

Q: Write down an equation of ARIMA (9,2,5) using y?

A: Given the time series process ARIMA9,2,5.

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: \f a,b and C. are 10 Lhen 2०-30)

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: choose 1 for each question: a) (1, 2, 3 , 4 , 5) b) (increase, decrease, or stay same) c) (up or…

A: The differential equation is y'=dydx=-(y+3)(y-1) has two points when y'=0, or, y=constant. If…

Q: {(r.0):3<rs4 and so<- Neatly sketch the set of points

A:

Q: At which of these times (A, B, C, D, E) was runner 1 stopped and runner 2 running? (Select all that…

A: From the graph it can be observed that, At time A the runner 1 had stopped and runner 2 was running,…

Q: if fcx) = _X then f (-1) is: |-X

A:

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

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

A: To find the following expressions

Q: uxv is , and U x u is

A: We are asked to find the cross product of the vectors

Q: j+ky-o Find k Iet yco)=lo0 andyc2)=4 3D0

A: Given that y'+ky=0 y(0)=100 and y(2)=4

Q: 5. Let A 3D, В %3 and C %3 Find a) (A · B)C b) А : (2С) c) ||B||2

A:

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

A:

Q: Let A = ff, I, y }, B = {r, a, t}. Find A x B and B X A. AxB= qafhbuifsfvggbh

A:

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

A:

Q: 5. For ea three c and be a)

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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

A:

Q: If a = (2, 0, 2), b =(4, 2,-2), and c = ax (bx c) = (a x b) x c = = (0, 2, 5), show that a x (bx c)…

A: The answer is in step2.

Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

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Q: Refer to B={ ={₁0, -6, 0.23, 3, -1.7, √7}. Determine which elements belong to the given set.…

A:

Q: 3) Let x = (-1,3,2,-4), and y = (1,0,2,3). Find the following distances || x = || = ? []x - || =?

A:

Q: 13. Find B x A, if A = {0,1,2} and B = {a, b}

A: B×A={ (x,y) : x€B and y€A}

Q: Q. One of the following statements is wrong: a. [-1,0] = [1,100] b.(2,3] = [-2,5) с. (1,2) %3DR…

A:

Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: Let u = and v = Find each quantity: a) (u)(v)  b) (u)(u)  c) (v)(v)

A: Given: u =&lt;4,-3&gt; and v =&lt;-2,7&gt;

Q: Find Range and Null space.

A:

Q: If u x = [1, -3,5], thenx =

A: