Relations and F...

If \(A=\left\{x \in R: x^{2}-7 x+12=0\right\}\) and \(B=\left\{y \in R: y^{2}-11 y+30=0\right\}\), then find the value of \(A\times B\)?

If \(A\) and \(B\) are the domain and range respectively for the relation \(R\) such that \(R=\{(1,3)\), \((2,4),(3,5),(5,7)\}\), then which of the following option is true?

Let \(A=\{x, y, z\}\) and \(B=\{1,2,3,4,5\}\). What is the number of elements in \(A \times B\)?

Find the domain of the function \(f(x)=\frac{1}{2-\sin 3 x}\).

If \(A=\{2,3\}, B=\{4,5\}, C=\{5,6\}\), then what is the number of elements in \(A \times(B \cap C) ?\)

If \(A=\left\{x \in R : x^{2}=2\right\}\) and \(B=\left\{y \in R : y^{2}-5 y+6=0\right\}.\) Find \(n(A \times B)\).

Let \(A\) and \(B\) be two sets such that \(A \times B\) consists of 6 elements. If three elements of \(A \times B\) are: \((1,4),(2,6),(3,6)\). Find the value of \(B \times A\).

If \(A=\{1,2,3,4,5,6\}\) and \(R\) is a relation on \(A\) such that \(R=\{(x, y): y=x+1\), where \(x\) and \(y \in R\}\), then find the domain of \(R\)?

If \(A=\{1,2,3,4,6\}\) and \(R\) is a relation on \(A\) such that \(R=\{(a, b): a, b \in A\) and \(b\) is exactly divisible by \(a\}\), then find the number of elements present in range of \(R\).

If \(x, y \in\{1,2,3,4\}\), then which of the following are functions in the given set?