Let A = {1, 2, 3), B = {4, 5, 6, 7) and let f = {(1, 4), (2,5), (3, 6)

1.	Let A = {1, 2, 3), B = {4, 5, 6, 7) and let f = {(1, 4), (2,5), (3, 6)} be a function from A to B. State whether f is one-one.
Answer» To state: Whether f is one-one Given: f = {(1, 4), (2,5), (3, 6)} Here the function is defined from A → B For a function to be one-one if the images of distinct elements of A under f are distinct i.e. 1,2 and 3 must have a distinct image. From f = {(1, 4), (2, 5), (3, 6)} we can see that 1, 2 and 3 have distinct image. Therefore f is one-one f is one-one

Let A = {1, 2, 3), B = {4, 5, 6, 7) and let f = {(1, 4), (2,5), (3, 6)} be a function from A to B. State whether f is one-one.

Answer»

To state: Whether f is one-one

Given: f = {(1, 4), (2,5), (3, 6)}

Here the function is defined from A → B

For a function to be one-one if the images of distinct elements of A under f are distinct

i.e. 1,2 and 3 must have a distinct image.

From f = {(1, 4), (2, 5), (3, 6)} we can see that 1, 2 and 3 have distinct image.

Therefore f is one-one

f is one-one