To determine which allele combination represents a male with an X-linked recessive disorder, we need to understand how X-linked inheritance works.
### Step-by-Step Explanation:
1. Chromosome Basics:
- Humans typically have 46 chromosomes, including 2 sex chromosomes (X and Y).
- Females have two X chromosomes (XX).
- Males have one X and one Y chromosome (XY).
2. X-linked Recessive Inheritance:
- An X-linked recessive disorder is caused by a recessive allele on the X chromosome.
- For a male to have an X-linked disorder, he only needs one copy of the recessive allele because he has only one X chromosome.
3. Notation:
- Let’s denote the normal allele as [tex]\(X^R\)[/tex] (R for the normal allele).
- The recessive allele causing the disorder is denoted as [tex]\(X^{\prime}\)[/tex] (prime for the recessive allele).
4. Possible Genotypes:
- For a male, the genotypes involving X and Y chromosomes are:
- [tex]\(X^{\prime}Y\)[/tex] (has the X-linked recessive allele, hence manifests the disorder)
- [tex]\(X^R Y\)[/tex] (has the normal allele, no disorder)
### Evaluating the Given Options:
- [tex]\(X^{\prime} Y\)[/tex]:
- This represents a male with one X chromosome carrying the recessive allele ([tex]\(X^{\prime}\)[/tex]) and one Y chromosome.
- Since [tex]\(X^{\prime}\)[/tex] is the allele causing the disorder, a male with [tex]\(X^{\prime}Y\)[/tex] will certainly have the disorder.
- [tex]\(X^R Y\)[/tex]:
- This indicates a male with one normal allele [tex]\(X^R\)[/tex] on the X chromosome and one Y chromosome.
- This individual will not have the disorder since [tex]\(X^R\)[/tex] is the normal allele.
- [tex]\(X^{\prime} X^r\)[/tex]:
- This is an impossible combination for a male because this genotype has two X chromosomes and no Y chromosome.
- Hence, this combination describes a female.
- [tex]\(X^R X^r\)[/tex]:
- This combination also suggests two X chromosomes, which is characteristic of a female.
- This genotype describes a carrier female (normal allele [tex]\(X^R\)[/tex] and recessive allele [tex]\(X^r\)[/tex]), not a male.
### Conclusion:
The allele combination that represents a male with an X-linked recessive disorder is [tex]\(X^{\prime} Y\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{X^{\prime} Y} \][/tex]
