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The candle flame danced to a frenzy as the crooning voice of Teresa Teng’s 《The Moon Represents My Heart》 filled the air.
Holding the lithe figure of the maths tutor close to his battle-scarred chest, the Ah Beng hadn’t felt such indescribable joy in his life, not even when he defeated his arch-rival gang leader in a gang fight.
Gently lifting her chin to peer into her childlike face, he knew tonight belonged to them and them alone, as their lips slowly drew closer …
.
.
.
When he woke up from his drunken stupor, the strained voice of 王傑’s 《是否我真的一無所有》 filled the air.
A year had passed since the day he tried and failed to buy her that $12000 diamond ring, for with the current recession, he was unable to raise the money despite beating all his debtors to a pulp.
Oh if only she knew about the countless times he ‘reserved’ a parking lot for her via a dustbin, so that she didn’t have to hunt for one each time she came for tuition.
If only she was aware of the countless parking attendants he had chased away with his chopper, for he knew that she always tore her parking coupon to start 15 mins later.
If only she knew about the protection money he had paid to rival gangs, to ensure her safe passage through the rough neighbourhood.
Determined not to spend another lonely Valentine’s Day this year drinking 闷酒, the Ah Beng decided to end his agony once and for all by bravely asking her out on a date.
With his traditional mind, he could only think of impressing her with a big bouquet of 881 roses and treating her to a romantic candlelight dinner at his local nightclub. Anxious to find out if his idea would work, and applying his new-found knowledge he picked up from eavesdropping the tutor’s Sets & Venn Diagrams lesson last week, he gathered all the girls at his local nightclub for an impromptu survey.
In a group of 350 women he surveyed,
200 of them like roses on Valentine’s Day.
230 of them like candlelight dinners on Valentine’s Day.
Find, by means of Venn Diagram(s),
- the smallest possible % of women who like both roses and candlelight dinners.
- the largest possible % of women who like neither roses nor candlelight dinners.
If the results of this survey were to be believed, should the Ah Beng carry out his plan?
With the migration of Sets and the bubbly circles of Venn Diagrams to the new E-Maths Syllabus, EMath students now need to familiarize themselves with the basic notations and concepts stated at the end of this old A-Maths post
For this particular problem, when you’ve been asked to find the smallest/minimum or largest/maximum sizes of certain unions and/or intersections of two sets A and B in a Venn Diagram, the first thing you’ll need to consider are the three possible scenarios that can occur in a Venn Diagram involving two sets A and B.
4 Comments
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does the winner / first one to geth the right answer score a romantic candlelight dinner date with you tomorrow?
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How the heck do you show workings for this one?
Anyway,
1) If all ladies who like roses like dinners as well, then intersection = 0 people (since set representing ladies who want roses is a subset of ladies who want dinners). However, then there will be 430 people. Hence minimum intersection=
430- 350=80. %tage= 22.8% (3 sig fig)
2) Assuming all ladies who don't want dinners also don't want roses, maximum number of ladies who don't want both= 350-230= 120.
%tage= 34.3% (3 sig fig)
So which set do you fall into? ;D
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Yes Clarion, we women have been guilty on many occasions of not painting the full picture (being deliberate dao or otherwise :P)
So in this case (where two sets of data are given), the "full pictures" (i.e. our Venn Diagrams) are not shown. &there4 it's good to bear in mind the following three possible scenarios of Venn Diagrams involving two sets, in order for you to have a clearer picture of which scenario to apply for the various parts of the question:
Let R = {women who like roses} and C = {women who like candlelight dinners}.
Translating what's given in the question into geeky Set Language, we have:
no. of "women who like both roses and candlelight dinners"
= n(R ∩ C) → let this be m
no. of "women who like neither roses nor candlelight dinners"
= n( (R ∪ C)' ) → let this be n
You're spot-on in your initial check of:
(we can rule out the Disjoint Scenario)
n(R) + n(C) = 200 + 230 = 430 > n(ξ)
⇒ there MUST be an intersection
⇒ R ∩ C ≠
To illustrate what you've worked out in a Venn Diagram, in order for m to be minimum we should be looking at the usual Intersect Scenario (since the Subset Scenario actually maximizes R ∩ C)
From the diagram it's clear that:
200 − m + m + 230 − m + n = 350
⇒ m + n = 80
⇒ Min m = 80 (occurs when n = 0)
∴ smallest possible % of women who like both roses and candlelight dinners
= (80/350) x 100% ≈ 22.9% (3 sig. fig.)
To maximize n, we're looking to maximize the shaded area (R ∪ C)' in the Venn Diagram.
Hence we should be looking at the Subset Scenario, where like you said "those who don’t want dinners also don’t want roses":
So max n
= n(ξ) − n(R ∪ C)
= n(ξ) − n(C)
= 350 − 230
= 120
∴ largest possible % of women who like neither roses nor candlelight dinners
= (120/350) x 100% ≈ 34.3% (3 sig. fig.)
As for Miss Loi's set ... umm ... probably (R ∪ C)' heee ...
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Oh Daphne, the poor maths tutor had waited and waited at the tze char restaurant on Saturday night, but as you can see Clarion's solution only came in on Sunday night, and coupled with a 34.3% chance of her being unimpressed by roses or candlelight ... think our Ah Beng might have to wait for another year.