Final answer:
Both parents of the child are heterozygous (Aa) for the autosomal dominant trait of tongue-rolling, while the child is homozygous recessive (aa) and cannot roll their tongue. This occurs due to receiving one recessive allele from each parent.
Step-by-step explanation:
If a man and a woman can both roll their tongues, which is an autosomal dominant trait, but have a child who cannot roll their tongue, this indicates that both parents must be heterozygous (Aa) for the tongue-rolling allele. This means each parent carries one allele for tongue-rolling (A) and one allele for non-tongue-rolling (a). The child who cannot roll their tongue must have inherited the non-tongue-rolling allele (a) from each parent, resulting in a homozygous recessive genotype (aa).
To visualize this, we would draw two Punnett squares, one for each parent. Each square would show the dominant (A) and recessive (a) alleles that each parent could pass on. When these are crossed, the potential genotypes for their offspring are AA, Aa, aA, and aa. Since tongue-rolling is a dominant trait, only the child with the aa genotype will not be able to roll their tongue.
The genotypes for the family would be as follows:
- The man (parent 1) is Aa
- The woman (parent 2) is Aa
- The child is aa