From 1959 to 1961, the number of cases of short-limbed deformities in some Western European countries increased year by year, reaching a peak at the end of 1960 and the beginning of 1961. Retrospective inquiries to mothers of children with short-limbed deformities revealed that many had a history of taking thalidomide. Further data showed that the increase in the number of cases of short-limbed deformities was closely related to the growth in thalidomide sales over time, with the two peak periods separated by exactly one gestation period. After the ban on thalidomide, the birth rate of infants with short-limbed deformities also dropped sharply. The above research proved that thalidomide was the culprit behind the outbreak of short-limbed deformities. Based on this case, which of the following statements are correct?

Options:
A. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of concomitant variation in inductive reasoning.
B. The increase in thalidomide sales was synchronous with the lagged increase in the number of cases of short-limbed deformities, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of concomitant variation in inductive reasoning.
C. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of analogy in inductive reasoning.
D. After the cessation of thalidomide sales, there was still a low-level sporadic occurrence of short-limbed deformities in the population, suggesting that in addition to thalidomide, some unknown factors may also be involved in the occurrence of short-limbed deformities. This reasoning process is the method of residues in inductive reasoning.
E. After the cessation of thalidomide sales, the number of cases of short-limbed deformities decreased sharply in a lagged manner, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of concomitant variation in inductive reasoning.
F. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of agreement in inductive reasoning.
G. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of difference in inductive reasoning.
H. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of correlation in inductive reasoning.
I. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of elimination in inductive reasoning.
J. Mothers of children with short-limbed deformities often had a history of taking thalidomide, suggesting a relationship between thalidomide and the occurrence of short-limbed deformities. This reasoning process is the method of residual analysis in inductive reasoning.
Answer: F