## Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this rel

Question

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

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1 month 2021-09-16T14:38:06+00:00 2 Answers 0 views 0

1. ### R = {(x, y): y = x + 5, x is a natural number less than 4, x, y E N} The natural numbers less than 4 are 1, 2 and 3.

R = {(1, 6), (2, 7), (3, 8)}

The domain of R is the set of all first elements of the ordered pairs in the

relation.

Domain of = {1, 2, 3}

The range of R is the set of all second elements of the ordered pairs in the relation.

Range of R = {6, 7, 8}

2. ➡️The relation R is given by:

➡️R = {(x, y): y = x + 5, x is a natural number less than 4, x, y ∈ N}

➡️The natural numbers less than 4 are 1, 2, and 3.

➡️So,

➡️R = {(1, 6), (2, 7), (3, 8)}

➡️Now,

➡️The domain of R is the set of all first elements of the ordered pairs in the relation.

➡️Hence, Domain of R = {1, 2, 3}

➡️The range of R is the set of all second elements of the ordered pairs in the relation.

➡️Hence, Range of R = {6, 7, 8}