To determine which allele combination represents a female who is a carrier for an [tex]\(X\)[/tex]-linked recessive disorder, we first need to understand some basics about [tex]\(X\)[/tex]-linked inheritance:
1. [tex]\(X\)[/tex]-linked recessive disorder: This type of disorder is carried on the [tex]\(X\)[/tex] chromosome.
2. Carrier Female: A female is a carrier if she has one normal allele and one allele for the disorder on her [tex]\(X\)[/tex] chromosomes. Since females have two [tex]\(X\)[/tex] chromosomes (XX), carriers have one copy of the normal allele (denoted by [tex]\(X^R\)[/tex] if [tex]\(R\)[/tex] represents the normal allele) and one copy of the recessive allele (denoted by [tex]\(X^r\)[/tex] if [tex]\(r\)[/tex] represents the recessive allele).
Given the options:
1. [tex]\(X^R X^r\)[/tex]: This combination indicates that the female has one normal [tex]\(X\)[/tex] chromosome [tex]\( (X^R) \)[/tex] and one [tex]\(X\)[/tex] chromosome with the recessive allele for the disorder [tex]\( (X^r) \)[/tex]. This is the definition of a carrier for an [tex]\(X\)[/tex]-linked recessive disorder, as the female carries one copy of the allele causing the disorder.
2. [tex]\(X^{\top} X^{\top}\)[/tex]: This notation doesn't specify [tex]\(R\)[/tex] or [tex]\(r\)[/tex], so it's not clear what [tex]\(X^{\top}\)[/tex] represents. However, standard notation requires the use of specified alleles for clarity.
3. [tex]\(X^R Y\)[/tex]: This combination represents a male with a normal [tex]\(X\)[/tex] chromosome [tex]\( (X^R) \)[/tex] and a [tex]\(Y\)[/tex] chromosome. Males only have one [tex]\(X\)[/tex] chromosome, so they cannot be carriers, and thus this combination is not applicable.
4. [tex]\(X^{\top} Y\)[/tex]: Similar to [tex]\(X^{\top} X^{\top}\)[/tex], this exactly written combination does not specify the nature of the allele. Also, since it implies a male genotype due to the presence of the [tex]\(Y\)[/tex] chromosome, males can't be carriers of [tex]\(X\)[/tex]-linked disorders in the same sense females can be. They either have the disorder or they do not.
Given the definitions and analyses above, the female who is a carrier for an [tex]\(X\)[/tex]-linked recessive disorder would have the allele combination [tex]\(X^R X^r\)[/tex]. Thus, the correct answer is:
[tex]\[ X^R X^r \][/tex]
So, a female who is a carrier for an [tex]\(X\)[/tex]-linked recessive disorder has the combination [tex]\(X^R X^r\)[/tex]. This combination ensures that she carries one normal allele and one allele for the disorder.
