What is the intersection of A and the union of B and C?

[blunted]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

My answer: {c}

 

[jedishrfu]

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 }

 

[kevinferreira]

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

 

[blunted]

Thanks.