Question

a man with blood group A marries a woman with blood group O and their daughter has blood group O. Is this information enough to tell you which of the traits-blood group A or O-is dominant? why or why not?

Answer 1

This information is not enough to tell which of the traits-blood group A or O is dominant.
It is known that blood groups A and B are codominant, which means both will express if found together in a heterozygote. However, blood group O is recessive. But from this information, you can conclude that blood group O is dominant. Why is that so?
Let's imagine that father's genotype is AA and mothers' genotype OO and cross them:
Parents:               AA    x    OO
Offspring:      AO    AO   AO    AO
Since we have information that daughter has blood group O, we can conclude that O is dominant over A and mask it. This is not true! In this case, the daughter will have blood group A.

Mother's genotype surely is OO (because O allele is recessive, so to express a recessive trait both alleles must be recessive). But, the father cannot be AA, because it must give O allele to the daughter so she can have genotype OO and blood group O. So, the father's genotype is AO.  Let's take a look at that crossing:
Parents:         AO   x    OO
Offspring:   AO   AO   OO   OO
Thus, in this case, daughter can have genotype OO and blood group O.