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Give Complete Solutions! Problems: (1) Recall, A, Is The Alternating Subgroup Of S Le, The Subgroup

Give complete solutions! Problems: (1) Recall, A, is the alternating subgroup of S le, the subgroup consisting of even permutations. Let n > 3. Show that #A,= (Hint: this was discussed in class.) (2) Let kan be natural numbers. Determine the parity (even or odd) of a eyelic permutation in (0,... E S. (Hint: the answer depends on the party of (3) Let n be a natural number. Determine the parity of the permutation O ES defined by o(i) = n +1-i for i=1,...,n. (Hint: the answer depends on n.)