Answer:

Introduction:
The dihedral group D8 is the group of symmetries of a square. It consists of 8 elements, which are the eight possible transformations of the square that preserve its shape and size. These transformations include rotations and reflections.

Generators of D8:
A generator of a group is an element that, when combined with itself or with other generators, can generate all other elements of the group. In other words, a set of generators can be used to construct all the elements of the group through their combinations.

Minimal Number of Generators:
The minimal number of generators of a group is the smallest set of generators that can generate all the elements of the group. In the case of D8, we need to find the smallest set of generators that can generate all 8 elements of the group.

Explanation:
To determine the minimal number of generators for D8, we can analyze the symmetries of a square and observe their relationships.

Rotations:
There are four possible rotations of the square: 0 degrees, 90 degrees, 180 degrees, and 270 degrees. These rotations can be generated by a single rotation of 90 degrees. Therefore, a single rotation of 90 degrees is a generator for the rotations in D8.

Reflections:
There are four possible reflections of the square: horizontal, vertical, and two diagonal reflections. These reflections cannot be generated by any combination of rotations alone. Therefore, we need at least one reflection to generate all reflections in D8.

Combining Rotations and Reflections:
By combining the rotation of 90 degrees and one reflection, we can generate all eight elements of D8. For example, starting with the identity element (no rotation and no reflection), we can apply the rotation of 90 degrees to generate the other three rotations. Then, by applying the reflection, we can generate the four reflections.

Conclusion:
Based on the analysis above, we can see that a single rotation of 90 degrees and one reflection are sufficient to generate all eight elements of D8. Therefore, the minimal number of generators for D8 is 2 (option B).