# 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

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