Kepler used the precise observations of the positions and movements of the planets and labored many years to mathematically determine that the orbits of the six planets known at the time were in the shape of ellipses.

Galileo performed experiments about the motions of objects and looked for patterns in their data. For example, Galileo found that the period of a pendulum was independent of the mass and amplitude but was dependent on the length of the string and gravity.

Albert Einstein's special theory of relativity, which was published in 1905, is a good example of how physicists ask questions and form hypotheses. Einstein never did a single experiment in this field in the laboratory. He used mathematics in his work.

Peter Higgs postulated that the universe was permeated by a field (Higgs field) that contains numerous uniformly distributed particles called Higgs bosons that cluster around other particles moving through the field. The Large Hadron Collider proved the existence of Higgs bosons.

a) Describe deductive reasoning, including an example from one of the scientists above. Be sure to clearly explain your choice.

b) Describe inductive reasoning, including an example from one of the scientists above. Be sure to clearly explain your choice.