The Cartesian product A \times A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct?<br>1. It is possible to determine set A.<br>2. A \times A contains the element (3, 2).<br>Select the correct answer using the code given below:
- A. 1 <strong>ONLY</strong>
- B. 2 <strong>ONLY</strong>
- C. <strong>BOTH</strong> 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. <strong>BOTH</strong> 1 and 2
Explanation
If A \times A has 16 elements, A must have \sqrt{16} = 4 elements. The given elements in A \times A are (0,2) and (1,3), meaning their components 0, 1, 2, 3 must belong to A. Since there are exactly 4 elements, A = \{0, 1, 2, 3\}. Thus, set A is completely determined (Statement 1 is correct). Since 3 \in A and 2 \in A, the element (3,2) must be in A \times A (Statement 2 is correct).
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