1. Compute |(124)(3567)| and |(1235)(24567)|. 2. Determine whether (1243) (3521)

Question

1. Compute |(124)(3567)| and |(1235)(24567)|. 2. Determine whether (1243) (3521) is even or odd. 3. Let alpha and beta belong to Sn. Prove that alpha beta is even if and only if and fi are both even or both odd. 4. Give two reasons why the set of odd permutations in Sn, is not a subgroup of Sn. 5. A card-shuffling machine always rearranges cards in the same way relative to the order in which they are given to it. All of the hearts arranged in order from ace to king were put into the machine, and then they shuffled cards were put into the machine again to be shuffled. If the cards emerged in the order 10, 9, Q, 8, K, 3, 4, A, 5, J, 6, 2, 7, in what order were the cards after the first shuffle?

Explanation / Answer

(2) odd bcoz if we multiply 3*1 we always get even answer

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