Question

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, codomain and range.​

Answer 1

$\huge\underline\mathfrak\pink{♡Answer♡}$

➡️The relation R from A to A is given as:

➡️R = {(x, y): 3x – y = 0, where x, y ∈ A}

➡️= {(x, y): 3x = y, where x, y ∈ A}

➡️So,

➡️R = {(1, 3), (2, 6), (3, 9), (4, 12)}

➡️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, 4}

➡️The whole set A is the codomain of the relation R.

➡️Hence, 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.

➡️Hence, Range of R = {3, 6, 9, 12}

Answer 2

$\huge\underline{\overline{\mid{\bold{\red{ANSWER-}}\mid}}}$

The relation R from A to A is given as

R = {(x, y): 3x – y = 0, where x, y ∈ A}

i.e., R = {(x, y): 3x = y, where 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 codomainof 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}