MHB What Are the Areas of Shapes A, B, & C in the Figure?

[bergausstein]

in the figureView attachment 1105, the area of the interior of the rectangle represents set A, the triangle set B, the circle Set C, indicate the area represented by

a. $\displaystyle A\cup B$
b. $\displaystyle A\cap B$
c. $\displaystyle A\cap C$
d. $\displaystyle B\cup C$
e. $\displaystyle \left(A\cup B\right)\cap C'$
f. $\displaystyle \left(A\cup B\right)'\cap C$

I'm not sure if I drew the picture correctly because I'm using a black and white printed book.

any hints how to start the problem? thanks!

 

[MarkFL]

First, I would ask you if you understand the definitions of union, intersection, and complement?

Once you understand the meanings of these operations, you should be able to shade in the appropriate areas for each statement.

So, can you give a brief definition of the above operations?

 

[bergausstein]

yes I understood it. here are my answersView attachment 1106

please check if it is correct.

 

[MarkFL]

I find that c) and e) are not quite correct. Can you spot the missing areas?

 

[bergausstein]

for c, and e. i hope this one is correct.:)View attachment 1107

 

[MarkFL]

Yes, that looks good! (Sun)

 

[bergausstein]

thank you so much!:)(Clapping)