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Show that the relation R on N × N, defined by (a, b) R (c, d) such that a + d = b + c is an equivalent relation.

Show that the relation R on N × N, defined by (a, b) R (c, d) such that a + d = b + c is an equivalent relation.

Class 12 Manik Bhola March 02, 2024

Given: $\text{R}: \mathbb{N}\times \mathbb{N}\rightarrow \mathbb{N}\times \mathbb{N}$, defined by $(a, b)\; \text{R}…

Check whether f(x) is strictly increasing or decreasing.

Check whether f(x) is strictly increasing or decreasing.

Class 12 Manik Bhola February 16, 2024

(i) $f(x)=3x-2$ where $f: \mathbb{R}\rightarrow \mathbb{R}$ # Method 1: Let $x_1, \; x_2$ be any element of $\mathbb{…

If A = R - {3} and B = R - {1}. Let f: A → B such that f(x) = (x-2)/(x-3) for all x ∈ A. Then show that f is bijective.

If A = R - {3} and B = R - {1}. Let f: A → B such that f(x) = (x-2)/(x-3) for all x ∈ A. Then show that f is bijective.

Class 12 Manik Bhola February 13, 2024

Given:   $\hspace{0.3cm}A=\mathbb{R}-\{3\}$ $\hspace{0.3cm}B=\mathbb{R}-\{1\}$ $\hspace{0.3cm}f:A\rightarrow B$ s…

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