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 `0-` is dominant? Why or why not?

Explanation

No, it is not possible. The information provided is insufficient to draw any such conclusions.
A man with blood group A can either be homozygous (IA IA) or heterozygous (IA iO) for the group. These details are not available in the statement above. No details are available about group O.
Just because a trait appears in the daughter/son it need not be a dominant trait.
Explanation: Let.s take a known example:
A tall plant is crossed with a short plant. Four seeds produced from the crossing were planted and all the four off springs produced were short. Is this information enough to tell you which of the traits - tall or short - is dominant?
Not possible, right?
We know tallness is dominant. Short trait is recessive. 
Then, how is this possible?
It is possible only if the tall plant is heterozygous tall (Tt). 
`Tt xx tt` can produce seeds with Tt or tt. The four seeds that were chosen randomly had tt as its genotype.
So just by looking at the offspring without sufficient information, one cannot conclude if a given trait is dominant or recessive.