Sets Question. Part (a) ???? and for (b) (i) the answer = 15, (b) (ii), the answer is 50. Don't know how.
Please Help.
A survey of what days people shop was conducted: venn diagrams
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elementary-set-theory
1 Answers
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$37$ people shop on one day only. $48$ people shop on two days only. Since each of the $100$ people who was surveyed shops at least one day (else they wouldn't have been found at the market in the first place), this implies that if $x$ is the number of people who shop on all three days we have $37+48+x=100$. Carrying out the arithmetic we see $x=15$ shops on all three of the days, so your work for part (b)(i) is correct.
Now... among the $48$ people who shop on two days only, $28$ of them shop on saturday as one of those two days. This implies that the remaining $20$ of them don't shop on saturday and thus the two days that they shop on are friday and sunday.
To glean any additional information, we have to make an assumption based on the picture provided. It is heavily implied that since the circle labeled $F$ encompasses both of the remaining two circles that the set of people who shop on saturday or sunday is a subset of those people who shop on friday.
Since the survey was conducted on a single day, only the people who were present at the market on that day were able to participate. If there was someone who shops only on a single day and that day wasn't the same day the survey was being conducted, they wouldn't have been able to respond.
This information together implies that the survey was conducted on friday, and as such we learn that since the survey was conducted on friday, zero people had the opportunity to say they shop one day only on saturday, zero say shop one day only on sunday, and zero say they shop two days only on saturday and sunday.
Armed with this knowledge, we go back and recognize that the people who responded saying they shop on two days only, $28$ of them shop on saturday and friday, and $20$ of them shop on sunday and friday.
We can now figure out how many people from the survey shop on sunday by totaling the people who shop on only on two days (friday and sunday) and the people who shop all three days. This gives a total of $20+15=35$ people shopping on sunday (not $50$)