Confused regarding finding the value n in Venn diagram

Jan 2015
78
0
Egypt
Hello everyone,

I'm glad to find this forum. I'm studing IGCSE and I hope you guys can help me whenever I'm stuck in a question.

When asking to get the value n in. Venn diagram they answer is usually is to count the number and not to add them but in some other question i find the answer that by adding the numbers not counting them as I am used to which confuses me.

here is an example in the attached file asking for value n(A U B)

The correct answer is 21 . My answer is 3


How come he added them this when in other similar questions he just counted the numbers as I did?

Thank you very much in advance for your help.
 

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HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
3?? I have no idea how you got that! I really don't understand what you mean by "counting" versus "adding". First, do you understand what \(\displaystyle F\cup B\) means (there is no "A" in the problem)? It is the total number of things that are in F and in B. The diagram tells you that there ate 7 things that are in F but not in B, 2 things that are in B but not in F and 12 things that are in Both F and B. That is a total of 7+ 12+ 2= 21 things altogether. There are 7+ 12= 19 things in F because those are the two numbers inside the oval labeled "F". There are 2+ 12= 14 things that are in B. The purpose of the Venn diagram is to make sure that you don't just add 19 and 14 because that would be counting the 12 things that are in A and B twice.
 
Jan 2015
78
0
Egypt
Thank you hallsofivy for your reply.

I would give you an example which might show what I mean by counting versus adding .

In the file attached , the answer is 2 which means he only counted the numbers of (B intersect A prime) which were 45 and 49 and didn't add them . The answer was not 94.
 

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Last edited:

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
And that was because the problem asked for \(\displaystyle A'\cap B\) whereas your first problem asked for \(\displaystyle F\cup B\). Do you understand the difference?
 
Jan 2015
78
0
Egypt
Does that mean in intersection question I only count the numbers and in union questions I add them?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Do you know the definitions of \(\displaystyle A\cup B\), \(\displaystyle A\cap B\).
 
Jan 2015
78
0
Egypt
Yes I understand their concept