Please answer all thank you!

1. Define the relationships (, , =) if any among the following sets (30 points): (a) A = {x : 1 x < 4} (b) B = {x : 1 < x 4} (c) C = {x : 1 x < 4} (d) D = {x : 1 x 2 < 4} (e) E = {x : 0 x < 1 2 and 1 2 x 2} (f) Does x E N?

2. Let (30 points) X = {x I : 20 < x 20 and x 2 I} Y = {x I : 2 < x 28 and x 2 I} (a) What are X Y , X Y , X Y , Y X, (X Y ) (X Y ), and (X Y ) (X Y )? (b) Does X Y ) N? (c) Does (X Y ) (X Y ) N? (d) Does (X Y ) (X Y ) N

3. For the following functions (30 points) (a) y = f(x) = 3x 2 + 6 is it convex or concave? Show your answer for full credit. (b) y = f(x) = 2x + 3y = 42 is it convex or concave? Show your answer for full credit. 1 (c) y = f(x) = 3x + 2y = 42 is it convex or concave? Show your answer for full credit. (d) y = f(x) = 3x 3 27 is it convex or concave? Show your answer for full credit