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 Post subject: venn diagram problem
PostPosted: Sat, 16 Oct 2010 08:44:13 UTC 
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Posts: 17
In town of 500 people, 285 read Hindu and 212 read Indian express and 127read
Times of India 20 read Hindu and times of India and 29 read hindu and Indian
express and 35 read times of India and Indian express. 50 read no news paper.
Then how many read only one paper?


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 Post subject: Re: venn diagram problem
PostPosted: Sat, 16 Oct 2010 14:27:44 UTC 
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6616
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
shafreenz wrote:
In town of 500 people, 285 read Hindu and 212 read Indian express and 127read
Times of India 20 read Hindu and times of India and 29 read hindu and Indian
express and 35 read times of India and Indian express. 50 read no news paper.
Then how many read only one paper?


Inclusion-exclusion. Assuming "Hindu" , "Indian express" and "Times of India" are newspapers, first find how many people read all three.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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 Post subject: Re: venn diagram problem
PostPosted: Mon, 18 Oct 2010 22:32:49 UTC 
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Hello, shafreenz!

There must be a typo.
The numbers are not consistent.


Quote:
In a town of 500 people:

. . 285 read Hindu
. . 212 read Indian Express
. . 127 read Times of India

. . . . 29 read Hindu and Indian Express
. . . . 35 read Indian Express and Times of India
. . . . 20 read Hindu and Times of India

. . . . . . 50 read no newspapers.
.
How many read only one paper?

Since 50 read no newspaper, then 500 - 50 \:=\:450 read at least one paper.

. . That is: .n(H \cup I \cup T) \:=\:450


Formula: .n(H \cup I \cup T) \;=\;n(H) + n(I) + n(T)
. . . . . . . . . . . . . . . . . . . . . . - n(H\cap I) - n(I\cap T) - n(H\cap T)
. . . . . . . . . . . . . . . . . . . . . . . . . + n(H\cap I\cap T)

We have: .450 \;=\;285 + 212 + 127 - 29 - 35 - 20 + n(H\cap I\cap T)

. . . . . . . .450 \;=\;540 + n(H \cap I \cap T)


Hence: .n(H \cap I \cap T) \;=\;-90 .??



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 Post subject: Re:
PostPosted: Fri, 22 Oct 2010 11:19:39 UTC 
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Location: California
HIndu = 285TOI = 127IE = 212now H nd TOI both is = 20(Draw a Venn Diagram nd check all) . TOI nd IE both is = 35H nd IE both is = 29now suppose H , TOI nd IE all is = x ;so,only Hindu is = 285-20-29-x = 236-x ;only TOI is = 127-20-35-x = 72-x ;only IE is = 212-35-29-x = 148-x ;now, 236-x + 72-x + 148-x + 20 + 29 + 35 + x + 50 = 500 590 -2x = 500 so, x = 45this is the value who read all the 3 dailies.so,result is = 236-45 + 72-45 + 148-45 = 191 + 27 + 103 = 321.


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 Post subject:
PostPosted: Fri, 29 Oct 2010 17:14:03 UTC 
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Joined: Sat, 25 Sep 2010 10:38:05 UTC
Posts: 17
THANKS JUSTIN


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