The discussion revolves around a problem in set theory involving Venn diagrams. The universal set is defined as having 40 elements, with Set A containing 20 elements and Set B containing 17 elements. The relationship between the intersection of Sets A and B is given by the equation n(A∩B) = 1/2 n(A'∩B'). Participants are exploring how to determine the value of n(A∩B) based on these parameters.
The discussion is ongoing, with participants providing hints and suggestions for approaching the problem. Some have proposed using Venn diagrams to visualize the relationships between the sets, while others are attempting to set up simultaneous equations to solve for the unknowns. There is a recognition of the need for clearer definitions and expressions in the problem setup.
Participants note that the original assumptions about the number of elements outside the sets may not hold true in all cases. There is also mention of the stress related to homework deadlines, which may be influencing the clarity of reasoning.
Ascleipus said: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^^
Ascleipus said:so a∩b=3?
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
LCKurtz said: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 said: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