Determine whether these statements are true or false. a) E 0 b) 0E {0} c) {0} {0} d) {0} {0, {0}} e) {{0}} {{0}, (0}} 2. 2 points each Determine the cardinality of the following sets a) 0 b) {0} c) {0, {0}} d) {0, {0}, {0, {0}}} 3. 5 points State whether the following is True of False and explaining your reasoning for full credit: The cardinality of every set is always less than the cardinality of its powerset. Page < 2 of 2 ZOOM 3. 5 points State whether the following is True of False and explaining your reasoning for full credit: The cardinality of every set is always less than the cardinality of its powerset. 1 4. 3 points each Let A = {a,b,c,d,e} and B = {a,b,c,d,e,f,g,h}. Find: a) AUB b) AnB ) - d) - 5. 13 points Prove the following theorem, for all sets A,B and C. AU(BnC)= (AUB)n(AUC) 6. 2 points each Simplify these values. a) [1.1] b) [1.1] c) L-0.1] d) [-0.1] e) [2.99] f) [-2.99] Page < 2 of 2 ZOOM 4. 3 points each Let A = {a,b,c,d,e} and B = {a,b,c,d,e,f,g,h}. Find: a) AUB b) AnB ) - d) - 5. 13 points Prove the following theorem, for all sets A,B and C. AU(BnC) = (AUB)n(AUC) 6. 2 points each Simplify these values. a) [1.1] b) [1.1] c) L-0.1] d) [-0.1] e) [2.99] f) [-2.99] 7. 2 points each Determine whether each of these functions are a bijection from R to R. a) f(r) = -3r2 + 7 b) f(r) = r + 1 8. 6 points Prove of disprove this statement about floor functions. [a + y] = [a] + [y] for all real numbers r and y