E 5 e e280 exam 2 notes 1.pdf 1[6482].pdf X MA 322 HW3.pdf + V - x 0 0 file:///C:/Users/jrsta/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/4498/Attachments/4[64! * ' 1 . | 1 of 1 - + Fit to page ID Page view | A Read aloud Acd notes s e Problem 1 (2 pts): Cive recursive definitions of the function f : {1,2,...} > R, where (a) f(n) = 6n +3. (b) f(n) = 2(n + 1), (c) Sin) - 3" l} }{1} = 12 +1)(1 + 2). Problem 2 (2 pts): How many one-to-one functions are there from a set of cardinality 10 to sets with the following cardinalities? (a) 7 (b) 11. (c) 15; (d) 20. Problem 3 (3 pts): A palindrome is a string whose reversal is identical to the string. How many strings using lower-case letters a, b,..., 2 of length n. are palindromes? Problem 4 (3 pts): Let n be a positive integer. Show that among any group of n + 1 (not necessarily consecutive) positive integers there are at least two with the same reminder when they are divided by n. Type here to search A G dx 11:32 AM 2/25/20206 E a ee280 exam 2 notes 1.pdf 1[6482].pdf X + v - X 0 0 file:///C:/Users/jrsta/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/4498/Attachments/4[64! * ' 1 . Lotto - + Fit to page ID Page view | A Read aloud Acd notes : Problem 1 (2 pts): Give recursive definitions of the function 11,2.... } R, Where a fin) = 6n +3, ih fix = 216 +1) c fin = 3; din In-lin+2). Problem 2 (2 pts): How many one-to-one functions are there from a sel of cardinality 10 lo sols with the following cardinalities? (a) 7. (h) 11. (c) 15. (d) 20. Problem 3 (3 pts): A palindromie is a string WELL ZOOM i identical to the string. Tlow many string 11sing lower-case letters ... ... 2 of length n are palindromes? Problem 4 (3 pts): Let be a positive integer. Show that among any group of +1 (not nossarily consecutive positive integers there are at least two with the same reminder when they are divicleni by vi. Extra Problem (4 pts.): Doline recursively the function ONE defined R, where (a) f(n) = 6n +3. (b) f(n) = 2(n + 1), (c) Sin) - 3" l} }{1} = 12 +1)(1 + 2). Problem 2 (2 pts): How many one-to-one functions are there from a set of cardinality 10 to sets with the following cardinalities? (a) 7 (b) 11. (c) 15; (d) 20. Problem 3 (3 pts): A palindrome is a string whose reversal is identical to the string. How many strings using lower-case letters a, b,..., 2 of length n. are palindromes? Problem 4 (3 pts): Let n be a positive integer. Show that among any group of n + 1 (not necessarily consecutive) positive integers there are at least two with the same reminder when they are divided by n. Type here to search A G dx 11:32 AM 2/25/20206 E a ee280 exam 2 notes 1.pdf 1[6482].pdf X + v - X 0 0 file:///C:/Users/jrsta/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/4498/Attachments/4[64! * ' 1 . Lotto - + Fit to page ID Page view | A Read aloud Acd notes : Problem 1 (2 pts): Give recursive definitions of the function 11,2.... } R, Where a fin) = 6n +3, ih fix = 216 +1) c fin = 3; din In-lin+2). Problem 2 (2 pts): How many one-to-one functions are there from a sel of cardinality 10 lo sols with the following cardinalities? (a) 7. (h) 11. (c) 15. (d) 20. Problem 3 (3 pts): A palindromie is a string WELL ZOOM i identical to the string. Tlow many string 11sing lower-case letters ... ... 2 of length n are palindromes? Problem 4 (3 pts): Let be a positive integer. Show that among any group of +1 (not nossarily consecutive positive integers there are at least two with the same reminder when they are divicleni by vi. Extra Problem (4 pts.): Doline recursively the function ONE defined