The Cartesian product \(A \times A\) has 25 elements among which are found \((3,1)\), \((6,2)\), \((5,3)\). Which of the following statements is/are correct? I. It is possible to determine other elements of \(A \times A\). II. \((5,5) \in A \times A\) and \((1,3) \notin A \times A\). Select the answer using the code given below.
I only
Since \(|A \times A|=25\), \(|A|=5\). The given pairs \((3,1), (6,2), (5,3)\) already involve 5 distinct values \(\{1,2,3,5,6\}\), so \(A=\{1,2,3,5,6\}\) is fully determined, making statement I true. Since \(1, 3 \in A\), the pair \((1,3)\) does belong to \(A \times A\), so the claim in statement II that \((1,3) \notin A \times A\) is false.
Important Questions from Cartesian Product of Sets
Compute the cartesian components of the electric field at the point if the potential at any point is given by V = x (y2 - 4x2)?
- Which of the following is a universal set of $Q \times N$ and $N \times Q$?
