Amy S.

asked • 01/19/18

Sets (Venn Diagrams) Really need help asap!

There are 35 girls in a class. 18 of these girls are in Dance and 21 girls are in Band. Given that

ξ = {Girls in the class}

D = {Girls who are in Dance}

B = {Girls who are in Band}

(i) Find the smallest value of n(D ∩ B).

(ii) Express the following in set notation: {Girls who is neither in Dance nor Band}

I need step by step answers for the whole question as I am unsure how to get the smallest value for part (i). Can't the smallest value for part (i) be 0? 

1 Expert Answer


Lori C. answered • 01/19/18

New to Wyzant

Amy S.

Hi, thanks for your quick reply. So is the answer for part (i) 4? I still don't get why the value can't be a 0, 1, 2 or 3. Isn't there is also a possibility for the class to have all its students in either or both CCAs?
Could you provide step by step answers? :)


Lori C.

This problem only gave you options of girls in one or both of the groups.
If there were  3 girls who did not participate in either, there would be 4 subgroups:  Neither + Dance only + Band only + Both.  That must add to 35.
Since we know that Neither = 3, we can say that Dance only + Band only + Both = 32.
Adding 18 + 21 = 39.  so 39 - 32 = 7.  That means 7 is Both.
We still have to contend with the 18 and 21 requirements.  18-7 = 11 and 21-7 = 14.
This is what we have:
Neither         = 3
Dance only = 11
Band only =   14
Both        = 7      
Total      = 35.


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