Independence on only some cells of the contingency table

Question

I have two discrete variables with three values each, A,B, and C for one, and D,E, and F, for the other (for around 500 objects).

I am only interested to reject independence in three cells of the nine cells in the table,(A,D),(A,E), (B,D).

So I have three null hypothesis:

H_AD :  Pr(AD) <= Pr(A) P(D)

H_AE :  Pr(AE) <= Pr(A) P(E)

H_BD :  Pr(BD) <= Pr(B) P(D)

which also say that for those cells, the observed values are lower or equal than the expected values according to the marginals. If the null hypothesis can be rejected, then we have that, on at least of those cells, the observed counts are greater than the expected, with some confidence.

So what I do is to use the usual chi squared test, but instead of adding over all 9 cells, I sum over only 3 cells and only if the observation counts are above the expected ones. Then, I calculate the p-value using the chi squared distribution (one tail) with 4 degrees of freedom since all table cells still affect the answer.

Is it correct?