Step 1: Note what the four choices are actually permutations of.
All four options pair the same five labels A to E against the same five roman numerals I to V, just arranged differently, so this can be attacked by comparing the options against each other before even recalling the exact definitions in the figure.
Step 2: Find the pairing that most options agree on.
Options 1, 2 and 3 all place E against V, and only option 4 breaks that pattern by pairing E with IV. Since three out of four choices agree on E-V, that pairing is almost certainly correct, which lets us drop option 4 from consideration immediately.
Step 3: Narrow the remaining three choices using a second point of agreement.
Among the surviving options 1, 2 and 3, options 2 and 3 further agree with each other on A-II and D-I, while option 1 disagrees on both, pairing A with III and D with II. Two independent choices agreeing on the same pair is stronger evidence than a single lone choice, so option 1 can also be set aside, leaving only options 2 and 3 in the running.
Step 4: Resolve the last disagreement.
Options 2 and 3 differ only in how B and C are paired with III and IV, a straight swap of the two. That final step is settled by the actual correspondence given for the soil and water engineering sub-disciplines in the figure, which assigns B to IV and C to III, exactly the arrangement in option 3.
\[ \boxed{(A) - (II), (B) - (IV), (C) - (III), (D) - (I), (E) - (V)} \]