https://ibb.co/tHSZQnM

Forgot how to upload an IMG to here but the link takes you to the picture I snipped. It's a Venn diagram. The question is:
Over a period of 115 days, conditions were recorded as sunny or cloudy and warm or cold. Let S denote sunny days and W warm days. Of 75 sunny days, 55 were warm. There were only 25 cold and cloudy days. Make a Venn diagram showing the numbers in each region of the diagram.

I am just trying to wrap my head around this because the simple answers aren't what they are looking for. I guess I am just looking for someone to sorta help me make sense of this if possible. The links to video's the instructor has us watch weren't really helpful to be honest.

This post was edited by JustinKTHXBYE on Jan 26 2022 09:39pm

Maybe just write down cardinality of given sets and apply basic set theory formulas?

S = set of sunny days
C = set of cloudy says
w = set of warm days
c = set of cold days

Where S is the complement of C and w the complement of c.

Denote |A| the cardinality of any set A.

We have

|S| = 75
|C| = 115-75 = 40 (complement)
|S∩w| = 55 (given in text)
|C∩c| = 25 (given in text)




The left box in your diagram should be sunny but not warm, i.e. S\w = S - S∩w, yielding |S\w| = |S| - |S∩w| = 75-55 = 20.

The middle box in your diagram should be sunny and warm, i.e. |S∩w| = 55.

The right box in your diagram should be warm but no sunny, i.e. w\S = w - S∩w. We can get the set of warm days by S∩w + C∩w since S and W are complements. We further know C∩w + C∩c = C since w and c are complements.
Now |C| = |C∩w| + |C∩c|, i.e. 40 = |C∩w| + 25, such that |C∩w| = 15. By that |w| = |S∩w| + |C∩w| = 55 + 15 = 70. This leads to |w\S| = |w| - |S∩w| = 70 - 55 = 15.


Also in total 70 days were warm, |w| = 70.



All those annoying calculations can be easily seen in a 2x2 matrix:



The asterisks values were given in the text and then you easily get the remaining values by adding stuff up.

Write so people with normal intelligence understand pls 🤬

They tell you there are 115 days, so
(Total Sunny Days) + (Total Cloudy Days) = 115

But they also tell you that (Total Sunny Days) is 75, which means (Total Cloudy Days) is 40 using the above equation.

We also know.
(Cold Sunny) + (Warm Sunny) = (Total Sunny)
(Cold Cloudy) + (Warm Cloudy) = (Total Cloudy)

We previously calculated (Total Sunny Days) = 75 and (Total Cloudy Days) = 40.
They tell you (Warm Sunny) = 55
They also tell you (Cold Cloudy) = 25

Substituting these values into the bolded equations:
(Cold Sunny) + 55 = 75
25 + (Warm Cloudy) = 40.

Solving each equation gives:
(Cold Sunny) = 20
(Warm Cloudy) = 15

In the above work is an answer for every possible combo

Your professor most likely wanted you do a similar process by filling in venn diagrams, not algebra. I'd walk you through that but i have no clue how to upload like 6 venn diagrams so you can see them. My method is equivalent and you can use it to solve all problems of this type

This post was edited by Jon011684 on Mar 25 2022 12:45pm