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Question

Define a relation R on the set N of natural number by R= {(x,y):y=x+5,x is a natural number less than 4;x,y ϵ N}. Depict this relationship using roster form. Write down the domain and the range.

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Solution

Given
R= {(x,y);y=x+5,x<4;x,y ϵ N}

Finding Roster form
Natural numbers less than 4 are 1,2,3
Put x=1,2,3 in y=x+5 and we get y=6,7,8 respectively.
So, R= {(1,6),(2,7),(3,8)}

Domain of R
The domain of R is the set of all first elements of ordered pairs in relation R.
Hence, domain of R= {1,2,3}

Range of R
The range of R is set of second elements of ordered pairs in relation R.
Hence, range of R= {6,7,8}

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