Step 1: Understanding the Concept:
Soil science is divided into two primary branches: Pedology and Edaphology.
These branches study soils from different scientific perspectives.
Step 3: Detailed Explanation:
Let us define the scientific terms provided in the options:
1. Pedology (B): This branch of soil science studies soil in its natural environment.
It focuses on soil origin (genesis), morphology, mapping, and taxonomic classification.
Pedologists view soil as a natural body formed by weathering and geological processes.
2. Edaphology: This branch of soil science studies how soil properties affect living things, particularly plants and crop yields.
3. Petrology (A): This branch of geology studies rocks, including their origin, composition, structure, and classification.
4. Petrography (D): This is a sub-field of petrology that focuses on the detailed microscopic description and classification of rocks.
5. Pedagogy (C): This is the method and practice of teaching, completely unrelated to earth sciences.
Therefore, the science dealing with soil genesis and classification is Pedology.
Step 4: Final Answer:
The science is Pedology, corresponding to option (B).