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The best way to distinguish between these three scenarios is with examples.
Let's look at a cross of red-flowered plants (RR) with white-flowered plants (rr). All of the offspring would be Rr, right?
The difference between complete dominance, incomplete dominance, and codominance is in the phenotype expressed (and sometimes the convention used to express the genotype).
In our flower example, if we had a situation of complete dominance, the heterozygous flowers (Rr) would express red flowers. (The convention for showing dominance when studying Mendelian genetics is that the dominant factor is named with a capital letter; thus, we can assume red flowers are dominant over white.) The red trait has completely covered up the white trait, so the red trait is completely dominant.
If we had a situation of incomplete dominance, both genotypes would be expressed in an "intermediate" phenotype. For our flower example, the heterozygous (Rr) flowers would express pink flowers - something between red and white. (The convention for incomplete dominance is no different than complete dominance; the only way you'd know is if you get a third phenotype from heterozygous offspring that you didn't have in the homozygous parents, or if the instructions told you you were dealing with incomplete dominance.)
If we had the last situation, codominance, both genotypes would express themselves at the same time. In our example, the heterozygous flowers (Rr) would show red and white flowers (maybe they're striped or flecked red and white), with no mixing of color.
The most common example of codominance is with blood types. People can be A, B, AB, or O blood typed. A (Ia) and B (Ib) are codominant - that is, if they are present together, they both express themselves in an AB blood type. The recessive is expressed as "i," and a homozygous recessive person (ii) shows an O blood type.
The convention with showing codominant genes are to either show it with a tick (R and R') or show it with a capital letter, then a superscript letter to distinguish between the two or more codominant genes (such as Ia, Ib, although I haven't figured out superscripts in YA yet).
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