Question 14 Marks
If 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. Show that f is one-one.
Answer
View full question & answer→Given, A = {1, 2, 3}, B = {4, 5, 6, 7} and
f : A $\rightarrow$ B is defined as f = {(1, 4), (2, 5), (3, 6)} i.e. f(1) = 4, f(2) = 5 and f(3) = 6.
It can be seen that the images of distinct elements of A under f are distinct. So, f is one-one.In other words, no two elements of set A are associated with set B which implies that there is one to one correspondence between X and Y.
f : A $\rightarrow$ B is defined as f = {(1, 4), (2, 5), (3, 6)} i.e. f(1) = 4, f(2) = 5 and f(3) = 6.
It can be seen that the images of distinct elements of A under f are distinct. So, f is one-one.In other words, no two elements of set A are associated with set B which implies that there is one to one correspondence between X and Y.