For the sets A = {0, 1, 2, 3\, B = {2, 3}, C = {1, 2, 4}, Match List - I with List - II.
Choose the correct answer from the options given below:
Show Hint
Notice that set \(B = \{2, 3\}\) is a subset of \(A = \{0, 1, 2, 3\}\). Because \(B \subseteq A\), their union \(A \cup B\) must be equal to \(A\) itself. Therefore, C matches II, which immediately narrows down the options.
• Step 1: Understanding the Question: This question is based on basic operations of Set Theory. We are given three finite sets: \(A\), \(B\), and \(C\). We need to perform operations like Set Union, Set Intersection, and Set Difference, and then match the results with the options in List-II.
• Step 2: Key Formula or Approach:
- Union (\(\cup\)): Combines all unique elements from both sets.
- Intersection (\(\cap\)): Contains only elements common to both sets.
- Difference (\(-\)): Contains elements present in the first set but not in the second.
Let us evaluate each set operation in List-I.
• Step 3: Detailed Explanation:
Let us perform the calculations:
- A. \(A - B\):
We remove any elements of set \(B\) from set \(A\):
\[ A = \{0, 1, 2, 3\}, \quad B = \{2, 3\} \]
\[ A - B = \{0, 1\} \]
This matches with IV.
- B. \(B \cap C\):
We find the common elements between \(B\) and \(C\):
\[ B = \{2, 3\}, \quad C = \{1, 2, 4\} \]
The only common element is 2.
\[ B \cap C = \{2\} \]
This matches with I.
- C. \(A \cup B\):
We combine all elements from \(A\) and \(B\):
\[ A = \{0, 1, 2, 3\}, \quad B = \{2, 3\} \]
\[ A \cup B = \{0, 1, 2, 3\} = A \]
This matches with II.
- D. \(A \cap C\):
We find the common elements between \(A\) and \(C\):
\[ A = \{0, 1, 2, 3\}, \quad C = \{1, 2, 4\} \]
The common elements are 1 and 2.
\[ A \cap C = \{1, 2\} \]
This matches with III.
Summarizing the matching:
- A matches with IV
- B matches with I
- C matches with II
- D matches with III
Thus, the correct sequence is A-IV, B-I, C-II, D-III.
• Step 4: Final Answer: The correct option is (D).
