Question

Here is an instance of a relation R(A,B,C,D):

Please just explain the feedback so I can attempt to solve it on my own!

A	B	C	D
1	2	3	4
1	3	3	3
1	3	3	4
1	2	3	3
2	2	4	4
2	4	2	4
2	4	4	4
2	2	2	4

Which of the following multivalued dependencies does this instance of R satisfy?
A->> B

BD ->> C
D ->> AB

B->> AD

I already know it's not B-> AD as the Answer Selecion Feedback says the following:

Look at each pair of tuples that have the same values for the attributes on the left side of the MVD. Consider the two additional tuples created by swapping values for the attributes on the right side of the MVD. (You may wish to review the formal definition of an MVD.) Are those tuples both already in the relation? If not, the MVD is not satisfied.

So if I'm checking to see if the MVD A->> B satisfies the Relation R, I want to look at all values in A (since that is the LHS of the MVD) that are the same so in this case, it would be 1 and 2. The part where I'm stuck on is what do they mean by considering the 2 additional tuples created by swapping values for the attributes on the right-hand side of the MVD?

V has the same A values as T and U so V sub A equals T sub-A, furthermore, V has its B Values.

I then go back to the definition of MVD which says the following: For all Tuples T and U that are in Relation R, if T with the attributes A of T equal U for the attributes A of U. THen there exists a 3rd Tuple V in R that has the following properties:

Answer 1

Which of the following multi-valued dependencies does this instance of R satisfy?

I can't see that it satisfies any of them, there always seems to be something missing. C $\rightarrow$> B is multi-valued dependencies this instance of R satisfy.