If a set A has 16 elements, another set B has 17 elements and a third set C has 7 elements, then what is the maximum possible number of elements in the set A or (B U C)? Provide an example with number sets.

Question

If a set A￼ has 16 elements, another set B ￼ has 17 elements and a third set C has 7 elements, then what is the maximum possible number of elements in the set A or (B U C)? Provide an example with number sets.

anonymous · Answer

***If a set ￼A has 16 elements, another set B￼ has 17 elements and a third set C has 7 elements, then what is the maximum possible number of elements in the set A and (B U C)? Provide an example with number sets.

queelius · Answer

A AND (B OR C) = (A AND B) OR (A AND C)

queelius · Answer

We are given that A has 16 elements, and B 17, therefore their intersection is max of 16. Likewise, for (A AND C), their intersection is a max of 7.

Now, we must combine these with the OR. This may be tricky.

anonymous · Answer

So can does this problem need to be set up in a Venn Diagram in order to be understood better?

queelius · Answer

A venn will usually help. Try it.

zarkon · Answer

$$A\cap(B\cup C)\subseteq A$$

therefore 

$$|A\cap(B\cup C)|\leq |A|$$

queelius · Answer

I deleted my solution since it was clearly wrong -- I had the combined set be larger than A.

queelius · Answer

Zarkon's solution is correct. 16 is the maximum size.

zarkon · Answer

mine is not a solution...you are supposed to provide an example

anonymous · Answer

okay thanks!