Practicing Success
The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : |x2 − y2| < 16 is given by |
R = {(1, 1) (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)} {(2, 2), (3, 2), (4, 2), (2, 4)} {(3, 3), (4, 3), (5, 4), (3, 4)} None of these. |
None of these. |
We have R = $\left\{(x, y):\left|x^2-y^2\right|<16\right\}$ Let x = 1 ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|1-y^2\right|<16$ $\Rightarrow \left|y^2-1\right|<16 \Rightarrow y=1,2,3,4$ Let y = 2 ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|4-y^2\right|<16$ $\Rightarrow \left|y^2-4\right|<16 \Rightarrow y=1,2,3,4$ Let y = 3 ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|9-y^2\right|<16$ $\Rightarrow \left|y^2-9\right|<16 \Rightarrow y=1,2,3,4$ Let y = 4 ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|16-y^2\right|<16$ $\Rightarrow \left|y^2-16\right|<16 \Rightarrow y=1,2,3,4,5$ Let y = 5 ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|25-y^2\right|<16$ $\Rightarrow \left|y^2-25\right|<16 \Rightarrow y=4,5$ ∴ R {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (4, 4), (4, 5), (5, 4), (5, 5)}. ∴ The correct answer is (4). Hence (4) is the correct answer. |