Which of the following are logically equivalent to the statement "Some fuzzy rabbits do not have floppy ears." if U is the set of all rabbits, p(x) is the statement "x is fuzzy" , q(x) is the statement "“x has floppy ears", F is the set of all fuzzy rabbits, and E is the set of all rabbits with floppy ears? (Choose all that apply): I. FNE° + Ø. II. (Vx E U)(¬(p(x) → q(x))). III. Some rabbits with floppy ears are not fuzzy. IV. F°n E + Ø. V. Not all fuzzy rabbits have floppy ears. VI. (3x E U)(p(x) ^ ¬q(x)). VII. F°U E + U.

Prove: bd (s) = 5 TR-S bd (s) is a closed set

1. Use set identities to show that (A U B)n (BU A) = A where A and B are sets. Let A = {1,2, 3} and B = {{0}, {1}}. Find A × B. 2.

Let G = {-23, –7, -3, –1,1,3, 5, 7, 14, 27, 42}. Decide if the following statements are true/false. Give a support to your answer. (a) Vr E G : if I 7. (d) 3r, y E G : (r² - y² = 0) ^ (x > 10) ^ (y > 10).