Venn Diagram problem (Set Theory)

[LCKurtz]

This means that the yellow is 2x and the red is 17-x
and then i assume i use simultaneous equations to solve it, do tell me if I'm on the right track, but please no answer^^

Don't use 2x for the yellow. Use the fact that it all adds up to 40 to figure out how many are in the yellow.

 

[Ascleipus]

but in order to figure out the yellow i need the intersection don't I?
40-(37-x) must be more appropriate then if i am to use that it adds up to 40

 

[Ascleipus]

it seemed reasonable to do 40-(37-x)=(37-x)/2

if the yellow is 40-(37-x) and the union of the two sets is 37-x if divide that by two then i should have a functioning equation, right?

however that just solves x as being 10.333...

 

[ArcanaNoir]

so a∩b=3?

Yes!

but how did you derive the equation a'∩b'=(1/2)(40-(a+b+a∩b))? I would understand if the 1/2 wasn't there, but if the 1/2 isn't there then the whole method doesn't work

a'nb' does not equal (1/2)(40-(a+b+a∩b))

a'nb' does equal (40-(a+b+a∩b))

Since anb=(1/2)a'nb' ,

anb= (1/2)(40-(a+b+a∩b))

 

[Ascleipus]

of course! thanks so much after all that i miss that 1 detail haha that's 2 problems you've helped me with, thank you to everyone else that has attempted to help me as well much appreciated everyone! physics forums is brilliant, hope i can someday help others like you have helped me :)

 

[LCKurtz]

Don't use 2x for the yellow. Use the fact that it all adds up to 40 to figure out how many are in the yellow.

but in order to figure out the yellow i need the intersection don't I?
40-(37-x) must be more appropriate then if i am to use that it adds up to 40

Sorry, I wrote that in a hurry. Go ahead and use 2x then just add them all up:

x + (17-x) + (20-x) + 2x = 40.

That's all there is to it.