21. Prove: a. If and is in (a, b), then y = yo is a solution of on (a, b). f(x,yo)=0, a

Let A=[aij]23 where aij=i+j, and let B=[bij]34 where bij=2ij. If AB=[cij]24, write a formula for cij in terms of i and j.

13. If u = (4, -9, −1) and v = 4ỉ − 2j3 + k, determine each of the following: - a. u.v f. (2ū + v) × (ũ – 2v) -

ulo,3) = 1+ y U(x, o) = 1+x 2

Suppose that B is a point between A and C. Prove that AB−→ =AC−→

Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g. AND' h. D'n (AUB)

Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x> 5}. Find a. D' b. D-A c. P(A) d. A-D e. A x B f. Bx B g. And' h. D'n (AUB)

1. Let A = (-∞, -2], B = (-3,8], C = (5,25) and U = R. Find An B, AUC, C \ B. 2. Prove that AU(BNC) = (AUB) N (AUC).

2. Show that 4=x i+yj+k is irrotational.

Q13)