MHB Determine the location of the subset

  • Thread starter Thread starter mathlearn
  • Start date Start date
AI Thread Summary
The furniture store offers 40 types of furniture, with 26 being wood-free and 12 of those locally manufactured. Among the wood types, 9 are locally made, while 11 wood-containing types qualify for discounts. Additionally, there are 13 types of furniture that do not qualify for discounts. A Venn diagram is used to represent these relationships visually, indicating the subsets of locally manufactured and discounted furniture. The discussion focuses on accurately depicting these subsets in the diagram.
mathlearn
Messages
331
Reaction score
0
In a furniture store there are 40 types of furniture for sale. Among them 26 types are wood free and , out of the wood free types , 12 are locally manufactured.Furthermore, the number of locally manufactured types containing wood is 9

View attachment 5979

Problem

First I drew the relevant venn diagram.

ii.How many furniture types that contain wood are not manufactured locally? Done and updated the venn diagram

In this store , a discount is given to all locally manufactured types of furniture and to some types of furniture that are not manufactured locally. There are 11 types of furniture containing wood that qualify for discounts and there are 13 types of furniture that do not qualify for the discounts.

Where do i need help:

iii.In a copy of the venn daigram drawn in i above , draw a subset suitably to indicate the types of furniture that qualify for discounts , and include clearly all the given information in the copy.

I need help to determine the location of the subset.

Many Thanks :)
 

Attachments

  • set.png
    set.png
    5.8 KB · Views: 101
Mathematics news on Phys.org
Okay, let's look at the statement:

In this store , a discount is given to all locally manufactured types of furniture and to some types of furniture that are not manufactured locally.

This means our new subset should include ALL of the locally manufactured and some of each of the other two types:

View attachment 5980

Now, let's look at:

There are 11 types of furniture containing wood that qualify for discounts...

So, we need to make the following change:

View attachment 5981

And finally, let's look at:

...and there are 13 types of furniture that do not qualify for the discounts.

Hence, we need:

View attachment 5982

Does that all make sense?
 

Attachments

  • mathlearnvenn2a.png
    mathlearnvenn2a.png
    9.7 KB · Views: 106
  • mathlearnvenn2b.png
    mathlearnvenn2b.png
    9.6 KB · Views: 110
  • mathlearnvenn2c.png
    mathlearnvenn2c.png
    9.5 KB · Views: 103
Thank you very much (Smile)
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Back
Top