# Set question

• Jan 8th 2011, 09:04 AM
Natasha1
Set question
If U = {3, 4, 5} and U union V = {1,2,3,4,5}

The set V I am told must have the fewest number of members as possible. Am I right in thinking that the members of the set V must be:

V = {1, 2}
• Jan 8th 2011, 09:13 AM
Chris L T521
Quote:

Originally Posted by Natasha1
If U = {3, 4, 5} and U union V = {1,2,3,4,5}

The set V I am told must have the fewest number of members as possible. Am I right in thinking that the members of the set V must be:

V = {1, 2}

Yes, that's correct based on what you've been told.

However, I believe we have more options: V = {1,2} , {1,2,3}, {1,2,4}, {1,2,5}, {1,2,3,4}, {1,2,3,5}, {1,2,4,5}, or {1,2,3,4,5}.
• Jan 8th 2011, 09:17 AM
Natasha1
Thanks. I am just a little perplex because if V = {1, 2} would that not mean that there would actually not be any union.

You'd have U = {3, 4, 5} and V = {1, 2} but completely separate and not sharing any members...

I am a little confused
• Jan 8th 2011, 09:21 AM
Chris L T521
Quote:

Originally Posted by Natasha1
Thanks. I am just a little perplex because if V = {1, 2} would that not mean that there would actually not be any union.

You'd have U = {3, 4, 5} and V = {1, 2} but completely separate and not sharing any members...

I am a little confused

The union is defined to be: $\displaystyle A\cup B=\{x : x\in A\text{ or }x\in B\text{ or in both}.\}$. So it turns out that there doesn't need to be an overlap between two sets in order to take their union. If there is an overlap, you would count that element just once.

However, if you ended up taking the intersection, it would be empty because there are no common elements.
• Jan 8th 2011, 09:22 AM
Natasha1
many thanks