Question 7. Give an example of a set A, for which An [1,4] = AnN and A \ Z ‡ Ø.

9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (a) AUA = A. (b) BnB = B. (c) (An B)' = A'n B' (d) (A')' = A (e) A\B= (B\A)' (f) (A\B) n(B\A) = 0 (g) If An B = 0), then ACB. (h) B x A = A x B. (i) 0× A = 0 (j) (A\B) U (B\C) = A \ C. (k) (A\B) n (A\C) =A\(BUC)

-, answer the following questions: -w³ (w+2) ³ (w - 4) ³ (w - 3) Given m(w) w7 (w + 2) (w-3)³ (w +9)¹ Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. a) The domain of m in set notation and interval notation is: Set Notation: {w w is a real number and w Interval Notation: 0 (-∞, -9) U (-9, -2) U (-2, 0) U (0, 3) U (3, ∞0) b) The w-intercept(s) are: c) The vertical asymptotes of m are at w Write the answer(s) as just numbers separated by commas. d) m has a hole at the ordered pair: Write each hole as an ordered pair. Do not do any rounding until the final answer. e) The m(w)-intercept is: ODNE f) The end behavior of m is: RH: As w LH: As or wor → m(w) Om(w) -∞ (4,0) 8 -9,-2,0,3 Horizontal Asymptote: DNE Write the horizontal asymptote as y = # if it exists. If it doesn't exist, type DNE. OF 0, 9 (3,0), (-2, 607.247)

20200 ecc 7. Given sets A, B and C prove or disprove that B) U (B-C) = (A-C)_