For the composition table of a cyclic group shown below Which one of the…

Solution:

Identify the identity element: The row labeled a has entries (a, b, c, d), so a acts as the identity (a * x = x and x * a = x).

• Element b: b * b = a, so b has order 2 and cannot generate the whole group.

• Element c: c * c = b, c^3 = d, c^4 = a, so c has order 4 and is a generator.

• Element d: d * d = b, d^3 = c, d^4 = a, so d has order 4 and is a generator.

Conclusion: The elements of order 4 (the generators of this cyclic group) are c and d, so the correct choice names c and d as generators.