Algebra Simple Interval & Interval Notation

Math 301 Quiz A (Ch 1) 31 August 2023 (30 pts) Always show ALL work. 1. (6 pts) Let the universal set be U = fa; b; c; dg. Recall X = U X and jXj = the cardinality of X. FIND and LIST all subsets A of U such that jAj > A . Hint: First list ALL the subsets of U . 2. (6 pts) EXPRESS the set A = fx 2 R : jx 2j < 2gfx 2 R : x 3g as a simple interval, using algebra and eventually interval notation as needed. Show all work and simplify as much as possible. Sketches can be helpful. 3. (6 pts) For a real number r, let Ar = fr; r 1g. Also, let S = fx 2 R : (x + 3)(x 2) = 0g. (a) (2 pts) FIND the two elements of S. LABEL them s and t where s < t. (b) (2 pts) DETERMINE the set As At . (c) (2 pts) Let X = fab 2 R : (a; b) 2 As At g. DETERMINE the sum of the elements of X. 4. (6 pts) De…ne An = 1 n1 ; 2 n1 , 8n 2 N. Remember, each An is [ an interval. FIND An . SKETCH A1 , A2 , and A3 , to provide a n2N plausible argument for your conclusion about this in…nite union. 5. (6 pts) Let S = f1; f1gg. Mark the following statements correctly as either TRUE or FALSE. (a) (1 pt) f1g 2 S. (b) (1 pt) f1g S. (c) (1 pt) 1 S. (d) (1 pt) S n f1g = f1g. (e) (1 pt) f1g f1g = f1g. (f) (1 pt) jf1g f1gj = 1. 1