Let a be an element of a group. Suppose abs(a5) = 12. Show that abs(a) = 12 or abs(a) = 60.

Q100; The neutral (Identity) element for the group {Z, +} is 1. T F

How to complete the table using the binary operation as a group? Let, S={f,g,h,j}, and let the operation ⋄:S⋄S→S ⋄ f g h j f f g h j g         h         j

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3. Verify Test the properties of a group : Let G denote a set of all ordered pairs of real-valued numbers with nonzero first component. Define the operation * by the rule (a, b) * (c, d) = (ac, be + d), V(a, b), (c, d) e G %3D

Decide which of the elements 2,3, and 5 are generators of the group Z/6.

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