# Disjoint proof

Hi everyone,

Could someone please show me how to prove this?

## Homework Statement

Determine |A U B| in terms of |A| and |B| assuming that A and B are disjoint

## The Attempt at a Solution

I know that A U B must be finite because A and B are disjoint, but besides that I don't know how I would go about proving this.

Could someone please show me how to?

Thank you

## Answers and Replies

Related Calculus and Beyond Homework Help News on Phys.org
There are some intuitive ways to answer this...
(i) The easiest way is to draw a Venn diagram and see what you think the answer might be
(ii) Secondly (and more formally) you could formulate the answer in terms of 'indicator functions'

$$i_X(x)= \begin{cases} 0 & \mbox{if }x \notin X \\ 1 & \mbox{if }x \in X$$

Try the first part and then see if you can do the same via the second

Thank you very much

Regards

matt grime
Homework Helper
Just because A and B are disjoint, does not in any way imply that AuB is finite. Just count the elements (assuming both A and B are finite).

HallsofIvy