Question

2. If A is the set consisting first five natural numbers and
F= {(x,y)/xsy) is a relation is A, then find the range and
domain of R​

Answer 1

Step-by-step explanation:

Given:

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

\textbf{To find:}To find:

RR

\textbf{Solution:}Solution:

1\, < \,2,\;1\, < \,3,\;1\, < \,4,\;1\, < \,5\;\implies\;(1,2),(1,3),(1,4),(1,5)\,{\in}\,R1<2,1<3,1<4,1<5⟹(1,2),(1,3),(1,4),(1,5)∈R

2\, < \,3,\;2\, < \,4,\;2\, < \,5\;\implies\;(2,3),(2,4),(2,5)\,{\in}\,R2<3,2<4,2<5⟹(2,3),(2,4),(2,5)∈R

3\, < \,4,\;3\, < \,5\;\implies\;(3,4),(3,5)\,{\in}\,R3<4,3<5⟹(3,4),(3,5)∈R

4\, < \,5\;\implies\;(4,5)\,{\in}\,R4<5⟹(4,5)∈R

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