To figure out the distribution of cleft chin and no-cleft chin traits through different generations ([tex]$P$[/tex], [tex]$F_1$[/tex], and [tex]$F_2$[/tex]) based on Mendelian genetics, let's go through the description step-by-step:
1. [tex]$P$[/tex] Generation:
- We start with two true breeding parents. One parent has a dominant cleft chin (genotype PP) and the other has a recessive no-cleft chin (genotype pp).
2. [tex]$F_1$[/tex] Generation:
- When these two true breeding parents (PP and pp) are crossed, all the offspring will inherit one dominant allele from the parent with a cleft chin and one recessive allele from the no-cleft chin parent.
- Thus, all [tex]$F_1$[/tex] generation offspring will be heterozygous (Pp) and display the dominant cleft chin phenotype.
3. [tex]$F_2$[/tex] Generation:
- When [tex]$F_1$[/tex] individuals (Pp) are mated with each other, the potential genotypes of the offspring follow a Mendelian 3:1 ratio, seen as follows:
- 1 PP (homozygous dominant) : 2 Pp (heterozygous) : 1 pp (homozygous recessive)
- This results in phenotypes with cleft chin (PP or Pp) and no-cleft chin (pp), with a 3:1 ratio respectively.
Based on the above process:
- The [tex]$P$[/tex] generation will have one dominant cleft chin parent and one recessive no-cleft chin parent.
- The [tex]$F_1$[/tex] generation will have all individuals with cleft chins.
- The [tex]$F_2$[/tex] generation will include both phenotypes: 3 parts cleft chin to 1 part no-cleft chin.
Given these details:
- The [tex]$P$[/tex] generation will have both cleft chins and no-cleft chins.
- The [tex]$F_1$[/tex] generation will have all cleft chins.
- The [tex]$F_2$[/tex] generation will have a mix of cleft chins and no-cleft chins.
So, regarding the given statements:
- The statement "[tex]$P$[/tex] generation, [tex]$F_1$[/tex] generation, and [tex]$F_2$[/tex] generation will have all cleft chins" is False.
- The statement "[tex]$P$[/tex] generation, [tex]$F_1$[/tex] generation, and [tex]$F_2$[/tex] generation will have all no-cleft chins" is False.
- The statement "The [tex]$P$[/tex] generation and [tex]$F _1$[/tex] generation will have all cleft chins" is False.
- The statement "The [tex]$F_1$[/tex] generation will have all cleft chins" is True.
- The statement "The [tex]$P$[/tex] generation and [tex]$F _2$[/tex] generation will have all no-cleft chins" is False.
- The statement "The [tex]$P$[/tex] generation and [tex]$F _2$[/tex] generation will have cleft chins and no-cleft chins" is True.
- The statement "The [tex]$P$[/tex] generation, [tex]$F _1$[/tex] generation, and [tex]$F _2$[/tex] generation will have cleft chins and no-cleft chins" is False.
Thus, the correct checks matching the given problem are:
- The [tex]$F_1$[/tex] generation will have all cleft chins.
- The [tex]$P$[/tex] generation and [tex]$F_2$[/tex] generation will have cleft chins and no-cleft chins.
