Wednesday

July 23, 2014

July 23, 2014

Posted by **ann** on Thursday, April 14, 2011 at 1:11pm.

The answer in the book is 22. I do not understand how they got this. Could someone please help me? Thanks.

- Math -
**MathMate**, Thursday, April 14, 2011 at 1:41pmIt is not clear if you have learned the inclusion/exclusion principle. If you have, you can apply it without drawing the Venn diagram.

However, for a two-set problem like this, it is easier to draw a Venn diagram and solve accordingly.

There are three sets in a universal set E where the cardinality (i.e. total number of elements) |E|=35.

We are also given that for the set of green hats G, |G|=20.

We conclude therefore that for the set R, |R|=|E|-|G|=35-20=15.

Of the 35 hats, irrespective of colour, 18 of them have logos, so belong to the set L, where |L|=18.

We are required to find the set of hats which are either red, or has a logo, that is, the cardinality of the set R∪L, or |R∪L|.

Consider now the sets L and R.

Draw a Venn diagram for the two, with an intersection, i.e. both red and have a logo. We understand that |L∩R|=11.

So if you put in the Venn diagram 18 for L, 15 for R, and 11 for R∩L. You can calculate that L-R (i.e. with a logo but not red) is 18-11=7, and R-L (i.e. red but no logo) is 15-11=4.

So therefore

|R∪L| = 7+11+4 = 22.

- Math -
**ann**, Thursday, April 14, 2011 at 10:53pmThanks a lot.

- Math :) -
**MathMate**, Thursday, April 14, 2011 at 11:22pmYou're welcome!

**Related Questions**

math - A magician has 3 more red hats than black hats and 4 fewer purple hats ...

algebra - the student store sells schools supplies,hats,and t-shirts with NAMS ...

4th grade math - I have to make a table or list to solve these problems. 1. Tina...

Math - A bag of marbles contains only green and red marbles. All of the marbles ...

Math - Coach Coleman is ordering hats for this year's teams. There are 6 teams. ...

math 6 - Jillianknits hats for her family and friends. In the first week, she ...

math - You have 7 red marbles and 5 green marbles in a bag. You select one, do ...

English - 1. How about making a gift together? What do you say to making a gift ...

art-colors - what are all the different colors that mix to make other colors? ...

Algebra - Use the Quadratic equation to determine the last day that cowboy hats ...