Let R be the universal relation on a set X with more than one element. Then R is

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

The range of the function \({1\over 1-2sinx}\) is

The range of the function \(f(x) = \left| \left\lfloor x \right\rfloor - x \right| ,x \in R\)  is 

The rule f(x) = x² is a bijection if the domain and the co-domain are given by

If n(A) = 10 and \(n(A\cap B)=3,\) find \(n((A\cap B')\cap A).\)

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find \(n((A\cup B)\times(A\cap B)\times(A \triangle B))\)

If p(A) denotes the power set of A, then find \(n(P(P(P(\phi)))).\)

Compare and contrast the graph y = x² - 1, y = 4(x² - 1) and y = (4x)² = 1.

By using the same concept applied in previous example, graphs of y = sin x and y = sin 2x, and also their combined graphs are given figures (a), (b) and (c). The minimum and maximum values of sin x and sin 2x are the same. But they have different x-intercepts. The x-intercepts for y = sin x are \(\pm n\pi\) and for y = sin 2x are \(\pm{1\over 2}n\pi,\ n\in Z.\) ​​​

Let us now draw the graph of y = 2 sin ( x - 1 ) + 3.

Let f, g: \(R \rightarrow R\) be defined as f (x) = 2x -|x| and g(x) = 2x + |x|. find f o g.

If \(f:R\rightarrow R\)  is defined by f(x) = 2x- 3, prove that f is a bijection and find its inverse