116777
If \(A\) and \(B\) be two sets such that \(A \times B\) consists of 6 elements. If three elements \(A \times B\) are \((1,4)\) \((2,6)\) and \((3,6)\), find \(B \times A\).
1 \(\{(1,4),(1,6),(2,4),(2,6),(3,4),(3,6)\}\)
2 \(\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\)
3 \(\{(4,4),(6,6)\}\)
4 \(\{(4,1),(6,2) \cdot(6,3)\}\)
Explanation:
Given, A and B be two sets. And \((1,4),(2,6)\) and \((3,6)\) are the elements of \(A \times B\) Then by ordered pair 1, 2, 3 are the elements of \(A\) and 4,6 are the elements of \(B\). \(\therefore \mathrm{A}=\{1,2,3\}, \mathrm{B}=\{4,6\}\)So, \(\mathrm{B} \times \mathrm{A}=\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\) Ans: Exp:
VITEEE-2011
Sets, Relation and Function
116778
If \(A\) and \(B\) have \(n\) elements in common, then the number of elements common to \(A \times B\) and \(\mathbf{B} \times \mathbf{A}\) is
1 0
2 \(\mathrm{n}\)
3 \(2 \mathrm{n}\)
4 \(\mathrm{n}^2\)
Explanation:
D Given, A and B have \(\mathrm{n}\) elements in common. So, the number of elements common to \(\mathrm{A} \times \mathrm{B}\) and \(\mathrm{B} \times \mathrm{A}\) is \(\mathrm{n} \times \mathrm{n}=\mathrm{n}^2\)
116777
If \(A\) and \(B\) be two sets such that \(A \times B\) consists of 6 elements. If three elements \(A \times B\) are \((1,4)\) \((2,6)\) and \((3,6)\), find \(B \times A\).
1 \(\{(1,4),(1,6),(2,4),(2,6),(3,4),(3,6)\}\)
2 \(\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\)
3 \(\{(4,4),(6,6)\}\)
4 \(\{(4,1),(6,2) \cdot(6,3)\}\)
Explanation:
Given, A and B be two sets. And \((1,4),(2,6)\) and \((3,6)\) are the elements of \(A \times B\) Then by ordered pair 1, 2, 3 are the elements of \(A\) and 4,6 are the elements of \(B\). \(\therefore \mathrm{A}=\{1,2,3\}, \mathrm{B}=\{4,6\}\)So, \(\mathrm{B} \times \mathrm{A}=\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\) Ans: Exp:
VITEEE-2011
Sets, Relation and Function
116778
If \(A\) and \(B\) have \(n\) elements in common, then the number of elements common to \(A \times B\) and \(\mathbf{B} \times \mathbf{A}\) is
1 0
2 \(\mathrm{n}\)
3 \(2 \mathrm{n}\)
4 \(\mathrm{n}^2\)
Explanation:
D Given, A and B have \(\mathrm{n}\) elements in common. So, the number of elements common to \(\mathrm{A} \times \mathrm{B}\) and \(\mathrm{B} \times \mathrm{A}\) is \(\mathrm{n} \times \mathrm{n}=\mathrm{n}^2\)
116777
If \(A\) and \(B\) be two sets such that \(A \times B\) consists of 6 elements. If three elements \(A \times B\) are \((1,4)\) \((2,6)\) and \((3,6)\), find \(B \times A\).
1 \(\{(1,4),(1,6),(2,4),(2,6),(3,4),(3,6)\}\)
2 \(\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\)
3 \(\{(4,4),(6,6)\}\)
4 \(\{(4,1),(6,2) \cdot(6,3)\}\)
Explanation:
Given, A and B be two sets. And \((1,4),(2,6)\) and \((3,6)\) are the elements of \(A \times B\) Then by ordered pair 1, 2, 3 are the elements of \(A\) and 4,6 are the elements of \(B\). \(\therefore \mathrm{A}=\{1,2,3\}, \mathrm{B}=\{4,6\}\)So, \(\mathrm{B} \times \mathrm{A}=\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}\) Ans: Exp:
VITEEE-2011
Sets, Relation and Function
116778
If \(A\) and \(B\) have \(n\) elements in common, then the number of elements common to \(A \times B\) and \(\mathbf{B} \times \mathbf{A}\) is
1 0
2 \(\mathrm{n}\)
3 \(2 \mathrm{n}\)
4 \(\mathrm{n}^2\)
Explanation:
D Given, A and B have \(\mathrm{n}\) elements in common. So, the number of elements common to \(\mathrm{A} \times \mathrm{B}\) and \(\mathrm{B} \times \mathrm{A}\) is \(\mathrm{n} \times \mathrm{n}=\mathrm{n}^2\)
