Understanding the Calculation of Hospital Emergency Visits A ∩ B and A U B

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The discussion focuses on the calculations of hospital emergency visit events A ∩ B and A U B. Participants clarify that A ∩ B represents the intersection of events, while A U B represents their union. There is confusion regarding the inclusion of the number 242 in the calculations, which is identified as a typo that should be added. Additionally, the number 953 is correctly included in the union calculation, as it represents a specific subset of visits. Overall, the conversation highlights the importance of accurate data entry in statistical calculations.
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Homework Statement
A ∩ B and A U B
Relevant Equations
The question is taken from a Book. I don't understand how A ∩ B and AUB is calculated?
A ∩ B and A U B
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robax25 said:
I don't understand how A ∩ B and AUB is calculated?
The text in the first image describes the events A and B. In words, what does the event A ∩ B mean? What does the event A U B mean?

Per the forum rules, you must show some effort. I've cut you some slack here by not issuing a warning.
 
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
 
robax25 said:
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
The ##242## should be added. It looks like a typo.

##953## is the total number of LWBS, which is set ##B##.
 
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robax25 said:
The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
This is misreading their answer. They are saying that the count of ##A \cup B ## is 5292+953-195, not ##A \cap B##.
 
robax25 said:
If I calculate A u B = 5292 + 270 + 246 but there is 242 as well. why is not 242 added? The second question is that A ∩ B = 5292 +953 - 195 but why does he add 953 to the equation?
I agree with @PeroK .

5292 + 270 + 246 = 5808 , but Book has the result being 6050 .

Looking further, 6050 − 5808 = 242 .

So, clearly the 242 was omitted mistakenly.
 
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Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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