In humans, a cleft chin is dominant, and no-cleft is recessive. What will the generations look like? Assume that Mendel's method of crossing two true-breeding parents with opposite traits is followed. Check all that apply.

A. The [tex]$P$[/tex] generation, [tex]$F_1$[/tex] generation, and [tex]$F_2$[/tex] generation will have all cleft chins.
B. The [tex]$P$[/tex] generation, [tex]$F_1$[/tex] generation, and [tex]$F_2$[/tex] generation will have all no-cleft chins.
C. The [tex]$P$[/tex] generation and [tex]$F_1$[/tex] generation will have all cleft chins.
D. The [tex]$F_1$[/tex] generation will have all cleft chins.
E. The [tex]$P$[/tex] generation and [tex]$F_2$[/tex] generation will have all no-cleft chins.
F. The [tex]$P$[/tex] generation and [tex]$F_2$[/tex] generation will have cleft chins and no-cleft chins.
G. The [tex]$P$[/tex] generation, [tex]$F_1$[/tex] generation, and [tex]$F_2$[/tex] generation will have cleft chins and no-cleft chins.

To solve the given question, let's analyze the genetics step-by-step using the principles of Mendelian inheritance:

1. P Generation (Parental Generation):
- Let "C" represent the dominant allele for cleft chin.
- Let "c" represent the recessive allele for no-cleft chin.
- The P generation consists of crossing a homozygous dominant (CC) individual with a homozygous recessive (cc) individual.
- Punnett square illustration:
```
C C
------------
c | Cc | Cc |
c | Cc | Cc |
```
- The F1 generation offspring will be all heterozygous (Cc). Since the cleft gene "C" is dominant, all individuals in the F1 generation will have cleft chins.

2. F1 Generation (First Filial Generation):
- All individuals in the F1 generation are heterozygous (Cc).
- When these heterozygous individuals are self-crossed:
- Punnett square illustration:
```
C c
------------
C | CC | Cc |
------------
c | Cc | cc |
```
- The resulting genotypes in the F2 generation from this cross are: 1 CC (homozygous dominant), 2 Cc (heterozygous), and 1 cc (homozygous recessive).
- Phenotypes:
- 3 individuals will have cleft chins (1 CC + 2 Cc).
- 1 individual will have no-cleft chin (cc).

So, breaking it down:
- P Generation: Homozygous dominant x homozygous recessive, so all offspring in F1 have cleft chins (Cc).
- F1 Generation: All individuals have cleft chins (heterozygous).
- F2 Generation: When F1 individuals self-cross, the genotypic ratio is 1:2:1 (CC, Cc, cc), which translates to a phenotypic ratio of 3 cleft chins to 1 no-cleft chin.

Based on the analysis, the correct answers should indicate that:
- The P generation and F1 generation have all cleft chins.
- The F2 generation has a mixture of cleft chins and no-cleft chins in a 3:1 ratio.

Therefore, the correct options are:

- The [tex]$P$[/tex] generation and [tex]$F_1$[/tex] generation will have all cleft chins.
- The [tex]$F_1$[/tex] generation will have all cleft chins.

Summing up, the correct selected options are:
- Option 3: The [tex]$P$[/tex] generation and [tex]$F_1$[/tex] generation will have all cleft chins.
- Option 4: The [tex]$F_1$[/tex] generation will have all cleft chins.