# Basic sets question

1. Jan 9, 2013

### blunted

1. The problem statement, all variables and given/known data

A = {a,b,c} ; B U C = {c,d,e,f} ; (A∩B) U (C∩A) = ?

2. Relevant equations

3. The attempt at a solution

A U B U C = {a,b,c,d,e,f}
A ∩ {B U C } = {c}

Last edited: Jan 9, 2013
2. Jan 9, 2013

### Staff: Mentor

do it in steps:

- A intersect B = { ... }
- C intersect A = { ... }

then union the results

Oops just saw you don't have B or C so you need to do set relations as you've shown to get B union C in the mix.

So I think you're right, the answer is { c }

3. Jan 9, 2013

### kevinferreira

Let's just make it on an easy notation where intersection is multiplication and union is sum:
$$A\times B+C\times A=A\times(B+C)=A\times\left\{c,d,e,f\right\}=\left\{ c\right\}$$

4. Jan 9, 2013

Thanks.