The problem requires matching set operations performed on given sets with their corresponding results.

Set Definitions

Given sets:

• $A = \{0, 1, 2, 3\}$
• $B = \{2, 3\}$
• $C = \{1, 2, 4\}$

Matching List I with List II

Operation A: $A - B$

The set difference $A - B$ contains elements that are in set $A$ but not in set $B$.

• $A = \{0, 1, 2, 3\}$
• $B = \{2, 3\}$
• $A - B = \{0, 1\}$

The result $\{0, 1\}$ corresponds to IV in List II.

Operation B: $B \cap C$

The intersection $B \cap C$ contains elements that are common to both set $B$ and set $C$.

• $B = \{2, 3\}$
• $C = \{1, 2, 4\}$
• $B \cap C = \{2\}$

The result $\{2\}$ corresponds to I in List II.

Operation C: $A \cup B$

The union $A \cup B$ contains all distinct elements from both set $A$ and set $B$.

• $A = \{0, 1, 2, 3\}$
• $B = \{2, 3\}$
• $A \cup B = \{0, 1, 2, 3\}$

The result $\{0, 1, 2, 3\}$ is the same as set $A$, which corresponds to II in List II.

Operation D: $A \cap C$

The intersection $A \cap C$ contains elements that are common to both set $A$ and set $C$.

• $A = \{0, 1, 2, 3\}$
• $C = \{1, 2, 4\}$
• $A \cap C = \{1, 2\}$

The result $\{1, 2\}$ corresponds to III in List III.

Final Matching

Based on the calculations:

• A matches with IV ($A - B = \{0, 1\}$)
• B matches with I ($B \cap C = \{2\}$)
• C matches with II ($A \cup B = \{0, 1, 2, 3\} = A$)
• D matches with III ($A \cap C = \{1, 2\}$)

Therefore, the correct matching is A-IV, B-I, C-II, D-III.