Answer:
The F₁ generation had all black and rough fur. Thus, black is dominant over white and rough is dominant over smooth.
Let us consider the two genes B and R for fur color and quality of fur respectively.
In gene B, B is the dominant allele which codes for black color and b is a recessive allele which codes for white color (when present in homozygous condition).
Similarly, in gene R, R is a dominant allele which codes for roughness and r being a recessive allele which codes for smooth fur (when present in homozygous condition).
So, the genotype of parents would be rrBB (smooth and black fur) and RRbb(rough and white fur).
The cross would result in the production of offspring all with rough and black fur that is, RrBb.
The selfing of F₁ generation would result in the production of offspring with four types of phenotypes; smooth white coats, smooth black coats, rough and white, and rough and black.
It shows that the alleles for the coat color and texture traits are inherited independently of each other.
The same is explained with the help of Punnett square in the below attachment.