Question

If A is the set consisting first five natural numbers and R= {(x, y)/x<y} is a relation in A, then find th
range and domain of R-​

Answer 1

$\textbf{Given:}$

$A=\{1,2,3,4,5\}\;\text{and}\;R=\{(x,y)/\;x\;<\;y\}$

$\textbf{To find:}$

$R$

$\textbf{Solution:}$

$1\,<\,2,\;1\,<\,3,\;1\,<\,4,\;1\,<\,5\;\implies\;(1,2),(1,3),(1,4),(1,5)\,{\in}\,R$

$2\,<\,3,\;2\,<\,4,\;2\,<\,5\;\implies\;(2,3),(2,4),(2,5)\,{\in}\,R$

$3\,<\,4,\;3\,<\,5\;\implies\;(3,4),(3,5)\,{\in}\,R$

$4\,<\,5\;\implies\;(4,5)\,{\in}\,R$

$\therefore\bf\,R=\{(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)\}$

Find more:

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Answer 2

Answer:

y=

2

10−x

where both x and y are natural numbers between 1 and 10.

Clearly for x= 2, 4, 6, 8 we get values of xy as 4, 3, 2, 1.

∴ R = ( 2, 4), (4, 3), (6, 2) (8, 1)}

∴R

−1

= {(4, 2) , (3, 4),(2, 6), (1, 8)}

Domain of R is {2, 4, 6, 8}= Range of R

1

Domain of R

−1

is { 4, 3, 2, 1} = Range of R

Step-by-step explanation:

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