Let A and B be distinct elements in T. Show that An BET. Case 1: A and B = R AnB =Øn R=Ø E T by a. Case 2: A = Ø and B = (-∞,a) Case 3: A =R and B = = (-∞,a) Case 4: A = (-∞,a) and B = (-∞,b) where a,b € R. WLOG, a > b.

Q: Which of the following are difference sets?

A: Introduction: A (v, k, λ) difference set is a k-element subset D of V = Z (mod v) in which any…

Q: 3. Given u =(3, 10,-8) and v = (-1,6,4), a) find 3v--u

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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) =…

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Q: Evaluate e/| 7xyz dS, where S is the triangle with vertices (1,0, 0), (0, 2, 0), and (0, 1, 1). (Use…

A: The complete solutions are given below

Q: Find the mid point for A( 1 , 2 ) B( 7, 8 )

A: Mid-point for the given points is- a=x1+x22,b=y1+y22 where a & b are the mid-points, and,…

Q: Let i = (2, –1, 5) and ū = (5, –7,3). Find 37 – 5ū. %3D - А. (-19, —32, 0) В. (-19, 32, 0) С. (19,…

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Q: lin +²-25 ++-5 2t² + 1lt +5

A:

Q: Haw:2 ExPress the Sumef the Vectars Aß and E ,if ACl,-), B (2,0)_, C(-1,)_ and D(-2,2).

A: Here is the solution

Q: 10. Find a and ẞ such that c = αa + ẞb, where a = (-3,0,2), b = (0,-1,2), and c = (-6,5,-10).

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Q: Show that if a > b, and a, b i= 0, then b- 1 > a - 1, provided that a and b have the same…

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Q: Let 10 0 B: 0 0 1 01 0 then find B2, B, B, B³ and B to figure out the pattern for B". Then find:…

A:

Q: Suppose ū = (-1,3,0) and v = (5, –2,5). Which of the following is 3v - u ? Select one: (-8,1,-5)…

A: given  u = (-1,3,0) v= (5,-2,5)

Q: a +b - la – b| 2 a+b+la-이 1. Prove: where max and min denote respectively the greater and the lesser…

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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.

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Q: 4 -7 6. 3. Determine the adjoint of -2 4 7 -4

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Q: 17. Show that Z () = zlog

A: Z-tramsform

Q: Given that 5w= (-5, 20), what is w? Select the correct answer below: O (-1,4) O (1, -20) O (-4,1) O…

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Q: uxv is , and U x u is

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

Q: Find JATI, JA³I, JATAI, and 16A|. -3 7 A = 5 1 (a) JATI -38 (b) JA³| (c) JATA| (d) 16A|

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Q: If A = {(x, y): (2, -2), (4, -1), (6, 0), . . .}, complete the rule for set A. y= 1/2x - 3 -1/2x -…

A: Observe the given pattern of set A then complete the rule.

Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: Is X and Y are independent

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Q: 9.) Find the value of b² – 4ac, given a = 4, b = 6, and c=-4.

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Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). - 2ü + 20 (-8,-12 - 20)

A: Given :-  u=<3,-4,-10>  v=<-7,-2,0>  To find:-  2u+2v

Q: 11. -a? - 2bc - Icl if a = -2, b = 3, and c = -3

A: Solution:

Q: If z,,z,€C then Zz=Z2 OZi+Z2=Z,+z2 OZi+z2=0 Z,Z2=0=Z,=0 or zz=0

A: 2nd and 4th options are correct.

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: given u = and v= find u*v

A: To find out the dot product u*v

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

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Q: 4. Ax (1-22, 1+22) where A - Z 5. Ax(0, 32, 62) where A - Z 6. A, [5, 10- +] where A = Z' 7. Ax (5+,…

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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: Which of the following are difference sets? (ii) {0, 1, 3, 5} in Z13,

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Q: Let A=[-1,7[,8={-1,3,10,12} and C={}}. Then (A-B) UC= *

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Q: (:) If rank of A is r and if B : , then the rank of B is: C ar O b. 2r Od.0

A: Given, the rank of matrix A is r. Then we have to find the rank of the matrix B=AA.

Q: Lot a,b,c be positive intergers, Prove that (ac, bc) = (9,b)c.

A: