In the given problem, we are analyzing the genetic makeup (genotypes) of a plant's stem length using two generations of Punnett squares. The dominant allele [tex]\(T\)[/tex] codes for a tall stem, while the recessive allele [tex]\(t\)[/tex] codes for a short stem. Here's a step-by-step analysis of the provided information:
### First Generation Punnett Square
The first-generation Punnett square is shown as follows:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
First Generation & t & t \\
\hline
T & Tt & Tt \\
\hline
T & Tt & Tt \\
\hline
\end{tabular}
\][/tex]
- Rows correspond to one parent's alleles.
- Columns correspond to the other parent's alleles.
- All resulting offspring genotypes in this square are [tex]\(Tt\)[/tex], indicating they are heterozygous (one [tex]\(T\)[/tex] allele and one [tex]\(t\)[/tex] allele).
### Second Generation Punnett Square
The second-generation Punnett square is shown as follows:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
Second Generation & T & t \\
\hline
T & TT & Tt \\
\hline
t & Tt & tt \\
\hline
\end{tabular}
\][/tex]
- Rows correspond to one parent's alleles.
- Columns correspond to the other parent's alleles.
- Offspring genotypes are [tex]\(TT\)[/tex], [tex]\(Tt\)[/tex], [tex]\(Tt\)[/tex], and [tex]\(tt\)[/tex].
### Analyzing the Statements
#### Statement: "Plants with short stems are homozygous for that trait."
This is true. Short stems are coded by two recessive alleles ([tex]\(tt\)[/tex]). If a plant has a short stem, it must have the genotype [tex]\(tt\)[/tex], which is homozygous recessive.
#### Statement: "Plants with tall stems are always homozygous for that trait."
This is false. Tall stems can be coded by either [tex]\(TT\)[/tex] (homozygous dominant) or [tex]\(Tt\)[/tex] (heterozygous). Both genotypes result in tall stems since the [tex]\(T\)[/tex] allele is dominant.
#### Statement: "Both parent plants in the second generation are heterozygous."
This is true. In the second-generation Punnett square, the alleles of the parent plants correspond to the labels on the rows and columns.
- One parent has [tex]\(T\)[/tex] and [tex]\(t\)[/tex] alleles.
- The other parent also has [tex]\(T\)[/tex] and [tex]\(t\)[/tex] alleles.
Thus, both parents have the genotype [tex]\(Tt\)[/tex], making them heterozygous.
#### Statement: "Both parent plants in the second generation are homozygous."
This is false. As described above, both parent plants have the genotype [tex]\(Tt\)[/tex] for the second generation, meaning they are heterozygous, not homozygous.
### Final Conclusion
Based on the analysis, the statements that are true about the genotype of the plants' stem length are:
1. Plants with short stems are homozygous for that trait.
2. Both parent plants in the second generation are heterozygous.
The resulting truth values for the statements in the question are:
1. True
2. False
3. True
4. False
