Is the following a Bijective Function?

$\begingroup$

In a bijective function is it necessary that all the elements of the domain correspond to a value in the range? Like for example can the following be a bijective function -

If not then what type of function is it?

$\endgroup$ 4

2 Answers

$\begingroup$

As per the diagram, it's not a function. A function assigns to every value $x$ in domain (which from the diagram seems to be the set $\{1,2,3,4,5,6\}$) a unique value in Co-domain (which seems to be equal to range from the diagram). Therefore, in your case, $f:\{1,2,3,4,5,6\}\to \{a_1,a_2,a_3,a_4\}$ is not a function.

However, if you consider restriction of $\{1,2,3,4,5,6\}$ to $\{1,2,3,4\}$, then yes, $g:\{1,2,3,4\}\to \{a_1,a_2,a_3,a_4\}$ is a bijection in the way your diagram shows.

$\endgroup$ $\begingroup$

This is a bijection from the set $\{1,2,3,4\}$ to the set $\{a_1,a_2,a_3,a_4\}.$

It is NOT a bijection from $\{1,2,3,4,5,6\}$ to $\{a_1,a_2,a_3,a_4\}.$

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy