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Solution

We have to match each normal form with the dependency that it removes or the property related to it.

First, consider $BCNF$.

$BCNF$ means Boyce-Codd Normal Form.

It is stronger than $3NF$.

A relation decomposed into $BCNF$ gives lossless decomposition, but it is not always dependency preserving.

So,

$A-(II)$

Now, consider $3NF$.

$3NF$ means Third Normal Form.

It removes transitive dependency.

In the question, it is written as transitive transparency, but the correct database term is transitive dependency.

So,

$B-(III)$

Now, consider $2NF$.

$2NF$ means Second Normal Form.

It removes partial functional dependency.

A relation is in $2NF$ when it is in $1NF$ and no non-prime attribute is partially dependent on a candidate key.

So,

$C-(IV)$

Now, consider $4NF$.

$4NF$ means Fourth Normal Form.

It removes multivalued dependency.

So,

$D-(I)$

Therefore, the correct matching is:

$(A)-(II), (B)-(III), (C)-(IV), (D)-(I)$