R= {(0, 1), (0, 2), (2,0), (2, 3), (4, 4), (2, 4), (3, 3), (1, 2), (1,3), (3 Evaluate dom(R), ran(R), R o R, R| R-1 IS1 RILLI and R-1[S1y

(1) If U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are neighborhoods of x0, so is ⋂ni-1U1

Let the universe U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 3, 4}, B = { n |n is odd}. Find %3D (AUB)' × A = ? O {(6, 2), (6, 3), (6, 4), (8, 2), (8, 3), (8, 4)} O {2, 3, 4, 5, 6, 8} {(2, 6), (2, 8),, (3, 6) (3, 8), (4, 6), (4, 8)} О (2, 3), (2, 4), (2, 6), (2, 8), (3, 3), (3, 4), (3, 6), (3, 8), (4, 6), (4, 8)}

If x + y + z = 1 and x, y, z are positive, then show that 2 (+ + +)* • (-+ +)* · · · ! )* > 100 + x+ +y+ +z+ X y Z 3

Let Aį = [i, i + 1], i = 1, 2, 3, .... Then A₁ A₂ A3 A4 is. a. {1,2,3,4,5} b. (1,5) c. {} d. [1,5] Ob Oc Od a

If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the reflexive closure of R? O {(1, 2), (2, 1). (1, 4), (4, 1). (2, 3), (3, 2), (3, 1). (1, 3), (4, 2), (2, 4)} O {(1, 1), (1, 2), (1, 4), (2, 2), (2, 3), (3, 1), (3, 3), (4, 2), (4, 4)} O {(1, 2), (1, 4), (2, 3). (3, 1), (4, 2)} O {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1). (3. 2). (3, 3), (3, 4), (4, 1), (4, 2). (4, 3), (4, 4)}

9. Given u = (2, -2), v = (5,8), and w = (-4, 3), find each of the following. (a) u v (b) (u. v)w (c) u. (2v) (d) ||w||²

How do I do this question?

Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive

1) Let u = (1,2,3), v = (2,2, -1), w = (4,0,-4). Find ||u-v+2w||.