what are the steps i have to take to find the sets that represent the red colored in the diagram?

Question

i tried using the notation to make it all separate and then see if i can put all the solution i get from each a,b, c together but i couldn't understand what i am doing wrong. if anyone could help with understanding this will be great, I have midterm coming up soon and i need to understand how these works. ven diagram

Answer 1

I love how you care about the steps more than the solution! These kind of problems require normally require you to 'Divide and Conquer'. You know some set operations like $A\cup B$ or $A \cap B$ or $A - B%$. I'd suggest drawing that diagram many times and color each of these possibilities. That is all 12 of these:

\begin{align*} A &\cup B & A &\cap B & A &- B & B &- A \\ B &\cup C & B &\cap C & B &- C & C &- B \\ C &\cup A & C &\cap A & C &- A & A &- C \end{align*}

It is a long process but doing this will get you a good idea of the "pieces" you can color. Once that you know which pieces you can color, you can combine these pieces by using the Union $\cup$. Since you probably have more problems I will tell you the solution: $(C-A)\cup (A\cap B$). Good luck!