Question

A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Relation R from A to A is given by R = {(x, y):y = x + 3}. Find domain, co-domain and range of R.

• A. Domain = {1, 2, 3, 4, 5, 6}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {4, 5, 6, 7, 8, 9}
• B. Domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {1, 2, 3, 4, 5, 6, 7, 8, 9}
• C. Domain = {1, 2, 3, 4, 5}, Co-domain = {6, 7, 8, 9}, Range = {6, 7, 8, 9}
• D. Domain = {2, 3, 4, 5, 6}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {4, 5, 6, 7, 8, 9}

Answer 1

The correct option is A

Domain = {1, 2, 3, 4, 5, 6}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {4, 5, 6, 7, 8, 9}

R = {(x, y): y = x + 3}

R = {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}

Domain is the set of first components of all the ordered pairs which belong to R.

Domain = {1, 2, 3, 4, 5, 6}

Co-domain is the set of all the elements of set B of the relation R.

Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Range is the set of second components of all the ordered pairs which belong to R.

Range = {4, 5, 6, 7, 8, 9}