Let A={1,2,3,....,14}. Define a relation R from A to A by R={(x,y):3x−y=0 where x,y∈A}. Write down its domain, co-domain and range.
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The relation R from A to A is given as
R={(x,y):3x−y=0;x,y∈A}
i.e., R={(x,y):3x=y;x,y∈A}
∴R={(1,3),(2,6),(3,9),(4,12)}
The domain of R is the set of all first elements of the ordered pairs in the relation
∴ Domain of R={1,2,3,4}
The whole set A is the co-domain of the relation R
∴ Codomain of R=A={1,2,3,.....,14}
The range of R is the set of all second elements of the ordered pairs in the relation.
∴ Range of R={3,6,9,12}
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