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Does this table show a binary operation? Yes No

Analyzing a binary operation table to determine if it defines a group, the existence of an identity element and inverses, and if it is abelian. The order of the group is also explored.

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Does this table show a binary operation? Yes No

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  1. Does this table show a binary operation? • Yes • No

  2. Is there an identity element? If so, what is it? • No (b) Yes, p • Yes, q (d) Yes, r • (e) Yes, s (f) Yes, t • (g) Yes, u (h) Yes, v • (i) Yes, w

  3. Does p have an inverse? • If so, what is it? • No (b) Yes, p • Yes, q (d) Yes, r • (e) Yes, s (f) Yes, t • (g) Yes, u (h) Yes, v • (i) Yes, w

  4. Does q have an inverse? • If so, what is it? • No (b) Yes, p • Yes, q (d) Yes, r • (e) Yes, s (f) Yes, t • (g) Yes, u (h) Yes, v • (i) Yes, w

  5. Does every element have an inverse? • Yes • No

  6. Does this table define a group? • Yes • No • I don’t know and if you think I am going to check associative you are out of your freaking mind.

  7. What is the order of this group? • 1 (b) 6 • 8 (d) 50 • (e) 64 (f) Primary

  8. Is this group abelian? • Yes • No

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