Are these venn diagrams correct for the problem?

[chijioke]

I am interested in knowing whether the venn diagrams are correctly drawn for each of the problems.
1.
2.

The following are the venn diagrams. I drew them by myself for each of the problems. Are they correct?
For the first problem we have:
For the second problem we have:

 

[stapel]

I am interested in knowing whether the venn diagrams are correctly drawn for each of the problems.
1.View attachment 36334

View attachment 36338

Assuming that "M" means "the number of men", "W" means "the number of women", and the overlap means "those who are paid weekly", you appear to have all 100 persons being male. Sixty men are paid weekly, and the other forty men are not.

Does this match the exercise?

2.
View attachment 36336

View attachment 36341

This Venn diagram looks good.

 

[chijioke]

Assuming that "M" means "the number of men", "W" means "the number of women", and the overlap means "those who are paid weekly", you appear to have all 100 persons being male. Sixty men are paid weekly, and the other forty men are not.

Does this match the exercise?



This Venn diagram looks good.

No. It doesn't. I am looking at it that venn diagram cannot be drawn for this kind of problem. What do you think?

 

[Dr.Peterson]

First problem:


I'm guessing that M means Men and W means Paid Weekly. Is that right? You must define your labels! (But what does [imath]\mu=100[/imath] mean?) If so, then women constitute everything outside the M loop, and those outside both loops are women who are not paid weekly (of which there are none).

(If M were Men and W were Women, you'd be saying that 60 people are both, which I'm sure you can't mean.)

Your diagram seems to say that there are 100 men (wrong), and that 60 of them, and no women (wrong) are paid weekly; it doesn't represent the fact that there are 65 men, or that all women are paid weekly.

Second problem:



This, as you've been told, is correct, assuming that M means "passed Mathematics" and P means "passed Physics"). I presume you can answer the questions from it.

No. It doesn't. I am looking at it that venn diagram cannot be drawn for this kind of problem. What do you think?

Why do you think it can't be drawn? And which problem are you referring to?

 

[Harry_the_cat]

To answer the question, a Venn diagram is not needed.
1. If there are 100 people and 65 are men, how many are women?
2. If 60 people are paid weekly, including all the ?? women, how many men are paid weekly?

A Venn diagram could look like:

where M is men and W is women.

 

[chijioke]

Why do you think it can't be drawn? And which problem are you referring to?

I have tried every manipulative skill to come up with a venn diagram suitable for the problem and yet nothing is fitting the problem as it is.

First problem:
View attachment 36342
View attachment 36343
I'm guessing that M means Men and W means Paid Weekly. Is that right? You must define your labels!

W means the set of women.

(But what does [imath]\mu=100[/imath] mean?)

It means all the men and women.

(If M were Men and W were Women,

Yes.

you'd be saying that 60 people are both, which I'm sure you can't mean.)

Your diagram seems to say that there are 100 men (wrong), and that 60 of them, and no women (wrong) are paid weekly; it doesn't represent the fact that there are 65 men, or that all women are paid weekly.

If 65 are men, then 35 would be women. All the 35 men and 25 women are paid weekly. So how do represent this in a Venn diagram or is it this not representable?

Second problem:
View attachment 36344
View attachment 36345

This, as you've been told, is correct, assuming that M means "passed Mathematics" and P means "passed Physics"). I presume you can answer the questions from it.


Why do you think it can't be drawn? And which problem are you referring to?

I have no issue with the second problem as it has been confirmed that it looks good. My focus is now on first problem.

 

[chijioke]

View attachment 36346
To answer the question, a Venn diagram is not needed.
1. If there are 100 people and 65 are men, how many are women?
2. If 60 people are paid weekly, including all the ?? women, how many men are paid weekly?

A Venn diagram could look like:
View attachment 36347
where M is men and W is women.

This is excellent. I love this.

Please if you have link where there are examples on various ways venn diagram can constructed please don't keep it away from me.

 

[Dr.Peterson]

I have tried every manipulative skill to come up with a venn diagram suitable for the problem and yet nothing is fitting the problem as it is.
W means the set of women.

But then you have no representation of "paid weekly".

If 65 are men, then 35 would be women. All the 35 men and 25 women are paid weekly. So how do represent this in a Venn diagram or is it this not representable?

The M loop contains men; everything outside it is women. You don't need a separate loop for them.

If we call the W loop "paid weekly", then we can do this:



There is are no women not paid weekly; so all the women (100 people - 65 men = 35 women) are paid weekly; then the rest of those paid weekly (60 - 35 = 25) are men who are paid weekly; and finally, the rest of the men (65 - 25 = 40) are not paid weekly.

This is a clearer diagram than the other. in my opinion.

 

[chijioke]

But then you have no representation of "paid weekly".


The M loop contains men; everything outside it is women. You don't need a separate loop for them.

If we call the W loop "paid weekly", then we can do this:

View attachment 36348

There is are no women not paid weekly; so all the women (100 people - 65 men = 35 women) are paid weekly; then the rest of those paid weekly (60 - 35 = 25) are men who are paid weekly; and finally, the rest of the men (65 - 25 = 40) are not paid weekly.

This is a clearer diagram than the other. in my opinion.

I appreciate the venn diagram but you did not label the rectangle which I suppose should be the universal set = 100.

 

[Dr.Peterson]

I appreciate the venn diagram but you did not label the rectangle which I suppose should be the universal set = 100.

Yes, I trusted that you knew that. If I deliberately cut off [imath]\mu=100[/imath], it would be because I'm not sure whether somehow [imath]\mu[/imath] means "size of universal set", and I didn't want to confuse things. (And you didn't label the universal set in your other diagram, so I take it to be optional.)

 

[chijioke]

Yes, I trusted that you knew that. If I deliberately cut off [imath]\mu=100[/imath], it would be because I'm not sure whether somehow [imath]\mu[/imath] means "size of universal set", and I didn't want to confuse things. (And you didn't label the universal set in your other diagram, so I take it to be optional.)

Now suppose I decide to give the information set notation, then this is what we expect:
n(M)=65 _total number of men)
n(MnW)=25_ meaning 25 men are working weekly and 25 women are working weekly as well)
n(M'nW) = 35 means...
Would I be right to say 35 represent all the women who are working weekly? Remember you said that N={ workers working on weekly basis including men and women}

 

[Dr.Peterson]

n(M)=65 (total number of men)

Yes, since M has been defined as the set of men.

I'm assuming you're using my definitions of M and W, not yours; namely M = set of men, W = set of people who are paid weekly.

n(MnW)=25 (meaning 25 men are working weekly and 25 women are working weekly as well)

No. The set [imath]M\cap W[/imath] is the set of people who are both men and paid weekly, that is, the set of men who are paid weekly. It says nothing about women.

Note: not working weekly, but paid weekly.

If you were using your definitions, with W = set of women, then [imath]M\cap W[/imath] would be the set of people who are both man and woman, which is empty.

n(M'nW) = 35 means...
Would I be right to say 35 represent all the women who are working weekly? Remember you said that N={ workers working on weekly basis including men and women}

Yes, with small corrections. This is the number of women who are paid weekly.

I said nothing about N, but, since M is the set of men, M' is the set of non-men, which we are presuming means women. (We aren't distinguishing children, for example.)

 

[chijioke]

Yes, since M has been defined as the set of men.

I'm assuming you're using my definitions of M and W, not yours; namely M = set of men, W = set of people who are paid weekly.

Yes

No. The set [imath]M\cap W[/imath] is the set of people who are both men and paid weekly, that is, the set of men who are paid weekly. It says nothing about women.

Note: not working weekly, but paid weekly.

If you were using your definitions, with W = set of women, then [imath]M\cap W[/imath] would be the set of people who are both man and woman, which is empty.

Yes, with small corrections. This is the number of women who are paid weekly.

Just an opportunity to correct my self using your diagram.





Would I be right to say 35 represent all the women who are paid weekly? Remember you said that W={ workers paid on weekly basis including men and women}
So what would you use to denote the number of men and women paid on weekly basis. Remember you did not give any label for women paid on weekly basis.

 

[Dr.Peterson]

Would I be right to say 35 represent all the women who are paid weekly? Remember you said that W={ workers paid on weekly basis including men and women}

Yes. The 35 is [imath]n(M'\cap W)[/imath], the number of women (i.e non-men) who are paid weekly.

So what would you use to denote the number of men and women paid on weekly basis. Remember you did not give any label for women paid on weekly basis.

That would be W! That's all people who are paid weekly.

 

[chijioke]

Thank you. I am now satisfied.