Let A be the set of first ten natural number. Let R be a binary relaion on A, defined by `R={(a,b):a,binA" and "a+2b=10}.` Express R and `R^(-1)` as sets of ordered pairs. Show that (i) dom (R)=range `(R^(-1))` (ii) range `(R)=dom(R^(-1))`.

Let A be the set of first ten natural number. Let R be a binary relaio

1.	Let A be the set of first ten natural number. Let R be a binary relaion on A, defined by `R={(a,b):a,binA" and "a+2b=10}.` Express R and `R^(-1)` as sets of ordered pairs. Show that (i) dom (R)=range `(R^(-1))` (ii) range `(R)=dom(R^(-1))`.
Answer» `a+2b=10b=((10-a))/(2).` Now, `(a=2impliesb=4),(a=4impliesb=3),(a=6impliesb=2),(a=8impliesb=1).` `:." "R={(2,4),(4,3),(6,2),(8,1)}` `implies" "R^(-1)={(4,2),(3,4),(2,6),(1,8)}.` `:." "dom(R)={2,4,6,8}="range "(R^(-1)).` (ii) range `(R)={4,3,2,1}=dom(R^(-1))`.

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Let A be the set of first ten natural number. Let R be a binary relaion on A, defined by `R={(a,b):a,binA" and "a+2b=10}.` Express R and `R^(-1)` as sets of ordered pairs. Show that (i) dom (R)=range `(R^(-1))` (ii) range `(R)=dom(R^(-1))`.

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