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NAME AND SURNAME Al E 1 The set G 1 3 5 7 is a...

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Algebra

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NAME AND SURNAME Al E 1 The set G 1 3 5 7 is a group with the operation zoy defined as the last decimal digit of the number 9x 9y zy 2 i Compute 505 0 505 ii Find the neutral element of o iii Find the inverse element 1 2 Let X be the set of all integers between 300 and 996 including 300 and 996 themselves that do not contain the digit 8 i How many elements does X have ii How many elements of X have three odd digits iii How many elements of X have three different digits 3 There are 12 blocks in a bag They have the following letters on them A A ADD GGGOOOO We choose 4 blocks from the bag and as we know there are 12 495 ways of doing that ie 495 four element subsets In how many of those 495 sets are there enough blocks to form the word DAD enough blocks to form the word DOG In this problem please write the actual numbers eg 24 rather than 2 3 4 questions for extra points Is the set G with the operation o described in Problem 1 above a group

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