To solve this problem, we need to determine how homozygous purelines in cattle can be obtained. Let's analyze each option:$\newline \bullet$Option 1: Mating of unrelated individuals of the same breed.$\newline$ - Mating unrelated individuals of the same breed increases genetic diversity and does not necessarily lead to homozygosity.$\newline \bullet$Option 2: Mating of individuals of different breeds.$\newline$ - Mating individuals of different breeds results in hybrid offspring, which are typically heterozygous.$\newline \bullet$Option 3: Mating of individuals of different species.$\newline$ - Mating individuals of different species is generally not possible due to reproductive barriers and does not produce purelines.$\newline \bullet$Option 4: Mating of related individuals of the same breed.$\newline$ - Mating related individuals of the same breed, also known as inbreeding, increases the chances of obtaining homozygous purelines as it reduces genetic variation.$\newline$Therefore, the correct option is Option 4: Mating of related individuals of the same breed.