Venn diagram: "Out of 25 teachers, 16 are married and 15 are women. If 6 of the men..."

[chijioke]

Definitions:
U={all the teachers}
M={men not married}
D={women not married}


Is my Venn diagram correct?

 

[blamocur]

I don't understand your diagram. In particular, what is the intersection of 'M' and 'D' ?

 

[Dr.Peterson]

View attachment 36359U={all the teachers}
M={men not married}
D={women not married}

View attachment 36360

The sets you show should represent one thing at a time; combining "men" and "not married" into the definition of one set complicates things.

Also, as in the other thread, you don't need separate sets for "men" and "women"; if you have one for men, then women are "not men" (that is, everything outside that set); you don't need a separate set for women.

I would have one for "men" and another for "married"; or, if you prefer, one for "women" and another for "single", so that the goal is to find the intersection of those.

 

[pka]

View attachment 36359

Suppose that [imath]A\text{ is the set of women teachers, }B\text{ is the set of men teachers and }C\text{ is the set of married teachers.} [/imath]
Note that [imath]\bf A \cap B = \emptyset [/imath] So [imath]\#(B\cap C)=6[/imath] , [imath]\#(A\cap C)=10[/imath]
[imath]\#(B\cap (A\cup C)^c)=4[/imath] and [imath]\#(A\cap (B\cup C)^c)=5[/imath]

 

[chijioke]

The sets you show should represent one thing at a time; combining "men" and "not married" into the definition of one set complicates things.

Also, as in the other thread, you don't need separate sets for "men" and "women"; if you have one for men, then women are "not men" (that is, everything outside that set); you don't need a separate set for women.

I would have one for "men" and another for "married"; or, if you prefer, one for "women" and another for "single", so that the goal is to find the intersection of those.

As I have shown in the diagram, 4 men and 5 women teachers are not married. 16 teachers both men and women are married. So the area outside show those who are married. They have nothing common. So that's why the intersection is an empty set.

 

[BigBeachBanana]

As I have shown in the diagram, 4 men and 5 women teachers are not married. 16 teachers both men and women are married. So the area outside show those who are married. They have nothing common. So that's why the intersection is an empty set.

I recommend making a 2-ways table for this problem, however, I have a feeling that you want to practice with Venn Diagrams and sets.

	Men	Women	Total
Married
Not married
Total

 

[Dr.Peterson]

As I have shown in the diagram, 4 men and 5 women teachers are not married. 16 teachers both men and women are married. So the area outside show those who are married. They have nothing common. So that's why the intersection is an empty set.

You have the right numbers. Unfortunately, the diagram doesn't show that, and in particular it is not useful in solving the problem or in showing that your solution is correct, because it has no place to show the 15 women or the 6 married men.

And the diagram is what you asked about:

View attachment 36359Definitions:
U={all the teachers}
M={men not married}
D={women not married}

View attachment 36360
Is my Venn diagram correct?

If your goal is to learn to make Venn diagrams, you have to correct it.

Is there a reason you choose not to follow my advice on how to do that?

 

[chijioke]

You have the right numbers. Unfortunately, the diagram doesn't show that, and in particular it is not useful in solving the problem or in showing that your solution is correct, because it has no place to show the 15 women or the 6 married men.

And the diagram is what you asked about:


If your goal is to learn to make Venn diagrams, you have to correct it.

Is there a reason you choose not to follow my advice on how to do that?

But the question demands of the women not married. Not the married ones.

 

[chijioke]

I recommend making a 2-ways table for this problem, however, I have a feeling that you want to practice with Venn Diagrams and sets.

	Men	Women	Total
Married	6	10	16
Not married	4	5	9
Total	10	15	25

But my Venn diagram is showing this already.

 

[Dr.Peterson]

But my Venn diagram is showing this already.

No, it doesn't make all of those numbers apparent. Several can't even be deduced from it. A proper diagram will show everything this table does.

But the question demands of the women not married. Not the married ones.

Why do you say this? The diagram I'd make shows everything you need:

M = married people
W = women

​

The unmarried women are [imath]M'\cap W[/imath].

Given that there are 6 married men ([imath]M\cap W'[/imath]), that leaves 16 - 6 = 10 women who are married, which leaves 15 - 10 = 5 women who are unmarried (the answer to the question, [imath]M'\cap W[/imath]); and the total is 21, leaving 4 who are neither married nor women.

All these numbers are in my diagram; only 4, 5, and 16 are in yours. You totally missed the distinction of men vs women who are married, and the set of all women.

This is because you did not use fundamental sets like women and married.

 

[Harry_the_cat]

The problem here is that you have two disjoint pairs of sets.
1. Men and women (ie these sets do not intersect with each other)
2. Married and Not-married (same here)

One way to represent this in a Venn diagram is to split the Universal set into two.

Venn Diagrams are not always the best way to represent data like this. A two-way table as in Post #6 would be more appropriate.
A bit like using a spanner to hammer in a nail!

 

[khansaheb]

A bit like using a spanner to hammer in a nail!

At least did not use a screw-driver!

 

[chijioke]

Thank you everybody for your interest in ensuring that I understand this Venn diagram concept. What I will do now is to go and study the previous thread and this very thread I created concerning Venn diagram construction and come with another thread to show that I have understood the concept. Thanks once again.