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

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 codomain 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}