While bone resorption can occur in the presence of a periapical granuloma, it is not a prerequisite for its formation. A periapical granuloma can develop in response to pulp necrosis or infection without necessarily requiring bone resorption to occur first. The granuloma can form as a reaction to the inflammatory process, regardless of the state of the surrounding bone.

1. Vitamin B12 deficiency resulting from inadequate intrinsic factor:
Vitamin B12 is an essential nutrient that plays a critical role in the production of healthy red blood cells. It is involved in the synthesis of DNA and the metabolism of fatty acids and amino acids. Intrinsic factor is a protein produced by the parietal cells of the stomach that binds to vitamin B12, allowing it to be absorbed in the small intestine. When there is a deficiency of intrinsic factor, vitamin B12 cannot be effectively absorbed from food, leading to vitamin B12 deficiency anemia. This is the most common cause of pernicious anemia.

Pernicious anemia is an autoimmune disorder where the body's immune system mistakenly attacks the stomach cells that produce intrinsic factor. Without sufficient intrinsic factor, vitamin B12 cannot be absorbed, resulting in a decrease in the number of red blood cells produced. The red blood cells that are formed are abnormally large and immature, known as megaloblasts. These cells are not efficient at carrying oxygen and are destroyed more quickly than normal cells, leading to the symptoms of anemia such as fatigue, weakness, and pallor. The deficiency in vitamin B12 can also affect the nervous system, causing neuropathy, cognitive impairment, and other neurological symptoms.

2. Folic acid deficiency resulting from inadequate intrinsic factor:
Folic acid is another B-vitamin essential for the production of red blood cells and is involved in DNA synthesis. However, folic acid deficiency is not directly caused by a lack of intrinsic factor. Folic acid is absorbed in the small intestine through a different mechanism than vitamin B12. While folic acid deficiency can also lead to megaloblastic anemia, it is not typically referred to as pernicious anemia. Pernicious anemia is specifically associated with vitamin B12 deficiency due to intrinsic factor deficiency or malabsorption.

3. Vitamin B12 deficiency resulting from inadequate extrinsic factor:
The term "extrinsic factor" is not commonly used in the context of vitamin B12 deficiency. Vitamin B12 is derived from dietary sources such as meat, fish, and dairy products. In the context of pernicious anemia, the issue is with the intrinsic factor, which is necessary for the absorption of vitamin B12. Therefore, this option is not accurate for explaining the cause of pernicious anemia.