Question 1123942
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<pre>
You should consider 4 sub-sets of the total set of 200 bracelets:


    - subset DR (have diamonds and rubies)   of 50 elements (bracelets);

    - subset DE (have diamonds and emeralds) of 70 elements (bracelets);

    - subset ER (have emeralds and rubies)   of 60 elements (bracelets);

    - subset DER (have diamonds, emeralds and rubies) of 20 elements (bracelets).
</pre>

<U>How many bracelets have emeralds ?</U>

<pre>     
      To find it, we should add the numbers DE and ER and then subtract DER :  DE + ER - DER = 70 + 60 - 20 = 110   (ANSWER).


          Why we should add  DE and ER, is clear to you without my explanations.
   
          Why we should subtract DER ?  - Because when we add DE and ER, we count DER twice.
</pre>

<U>How many bracelets have diamonds ?</U>

<pre>     
      To find it, we should add the numbers DR and DE and then subtract DER :  DR + DE - DER = 50 + 70 - 20 = 100   (ANSWER).


          Why we should add  DR and DE, is clear to you without my explanations.
   
          Why we should subtract DER?  - Because when we add DR and DE, we count DER twice.
</pre>

<U>How many bracelets have rubies ?></U>

<pre>
      Use the same logic and complete the solution on your own.
</pre>

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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

in this site.



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<U>comment from student</U>: This is wrong. The total number of bracelets is suppose to equal 200 and this equals 300
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<U>My response</U> :


<pre>
    My solution and my answers are correct !


    Your comment is WRONG.


    Why ?  - Because when you add the numbers, you count many bracelets twice and even thrice !
</pre>

Your tone/comment is very aggressive.  &nbsp;&nbsp;(Too aggressive to be polite . . . )


Please do not forget that you talk with the EXPERT.