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Sagot :
To solve this problem, we need to use a Punnett square to represent the cross between two plants with genotypes [tex]\( B b \)[/tex] and [tex]\( B b \)[/tex]. The Punnett square is a grid that shows all possible combinations of alleles from the parent plants.
1. Determine the possible gametes:
- Each parent plant can produce two kinds of gametes. Since both plants are [tex]\( B b \)[/tex], the possible gametes are [tex]\( B \)[/tex] and [tex]\( b \)[/tex].
2. Construct the Punnett square:
- We will create a 2x2 grid where each cell represents a possible combination of alleles.
3. Fill in the Punnett square:
- Write the alleles from one parent across the top and the other parent down the side. Typically, if we arrange it, it will look something like this:
```
B b
+-----+-----+
B | BB | Bb |
+-----+-----+
b | Bb | bb |
+-----+-----+
```
- Each cell inside the grid represents the combination of alleles from each parent.
4. Interpret the results:
- The cells contain the following combinations:
- Top left: [tex]\( BB \)[/tex]
- Top right: [tex]\( Bb \)[/tex]
- Bottom left: [tex]\( Bb \)[/tex]
- Bottom right: [tex]\( bb \)[/tex]
From the above Punnett square, we observe that the plants will have the following genotypes:
- 1 [tex]\( BB \)[/tex] (Broad leaves)
- 2 [tex]\( Bb \)[/tex] (Broad leaves)
- 1 [tex]\( bb \)[/tex] (Narrow leaves)
Now, let’s match this outcome with the provided options:
- Option A:
```
\begin{tabular}{|l|l|l|}
\hline & [tex]$B$[/tex] & [tex]$b$[/tex] \\
\hline [tex]$B B$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$B$[/tex] & [tex]$B b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This representation is incorrect because it does not match the standard layout of input/output gametes.
- Option B:
```
\begin{tabular}{l|l|l|}
\hline & \multicolumn{1}{c|}{[tex]$B$[/tex]} & [tex]$b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b$[/tex] & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline
\end{tabular}
```
This representation is also incorrect because it shows multiple identical entries that do not represent the correct combinations.
- Option C:
```
\begin{tabular}{|l|l|l|}
\multicolumn{1}{l}{} & \multicolumn{1}{c}{} & [tex]$b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This is incorrect because it does not list all unique combinations correctly, and [tex]\( BB \)[/tex] is missing entirely.
- Option D:
```
\begin{tabular}{l|l|l|}
\hline & \multicolumn{1}{|c|}{[tex]$b$[/tex]} \\
\hline [tex]$B$[/tex] & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b$[/tex] & [tex]$B b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This representation is correctly showing:
- [tex]\( BB \)[/tex] in the top left
- [tex]\( Bb \)[/tex] in top right and bottom left
- [tex]\( bb \)[/tex] in bottom right
Therefore, the correct Punnett square that represents the cross [tex]\( B b \times B b \)[/tex] is option D.
1. Determine the possible gametes:
- Each parent plant can produce two kinds of gametes. Since both plants are [tex]\( B b \)[/tex], the possible gametes are [tex]\( B \)[/tex] and [tex]\( b \)[/tex].
2. Construct the Punnett square:
- We will create a 2x2 grid where each cell represents a possible combination of alleles.
3. Fill in the Punnett square:
- Write the alleles from one parent across the top and the other parent down the side. Typically, if we arrange it, it will look something like this:
```
B b
+-----+-----+
B | BB | Bb |
+-----+-----+
b | Bb | bb |
+-----+-----+
```
- Each cell inside the grid represents the combination of alleles from each parent.
4. Interpret the results:
- The cells contain the following combinations:
- Top left: [tex]\( BB \)[/tex]
- Top right: [tex]\( Bb \)[/tex]
- Bottom left: [tex]\( Bb \)[/tex]
- Bottom right: [tex]\( bb \)[/tex]
From the above Punnett square, we observe that the plants will have the following genotypes:
- 1 [tex]\( BB \)[/tex] (Broad leaves)
- 2 [tex]\( Bb \)[/tex] (Broad leaves)
- 1 [tex]\( bb \)[/tex] (Narrow leaves)
Now, let’s match this outcome with the provided options:
- Option A:
```
\begin{tabular}{|l|l|l|}
\hline & [tex]$B$[/tex] & [tex]$b$[/tex] \\
\hline [tex]$B B$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$B$[/tex] & [tex]$B b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This representation is incorrect because it does not match the standard layout of input/output gametes.
- Option B:
```
\begin{tabular}{l|l|l|}
\hline & \multicolumn{1}{c|}{[tex]$B$[/tex]} & [tex]$b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b$[/tex] & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline
\end{tabular}
```
This representation is also incorrect because it shows multiple identical entries that do not represent the correct combinations.
- Option C:
```
\begin{tabular}{|l|l|l|}
\multicolumn{1}{l}{} & \multicolumn{1}{c}{} & [tex]$b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This is incorrect because it does not list all unique combinations correctly, and [tex]\( BB \)[/tex] is missing entirely.
- Option D:
```
\begin{tabular}{l|l|l|}
\hline & \multicolumn{1}{|c|}{[tex]$b$[/tex]} \\
\hline [tex]$B$[/tex] & [tex]$B b$[/tex] & [tex]$B b$[/tex] \\
\hline [tex]$b$[/tex] & [tex]$B b$[/tex] & [tex]$b b$[/tex] \\
\hline
\end{tabular}
```
This representation is correctly showing:
- [tex]\( BB \)[/tex] in the top left
- [tex]\( Bb \)[/tex] in top right and bottom left
- [tex]\( bb \)[/tex] in bottom right
Therefore, the correct Punnett square that represents the cross [tex]\( B b \times B b \)[/tex] is option D.
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