Nnamdi prices sweets in glass jars along the counter of his corner shop, from 20p to 29p, a penny apart. These ten prices are the universal set \(\mathscr{E...
Question 1 Report
Nnamdi prices sweets in glass jars along the counter of his corner shop, from 20p to 29p, a penny apart. These ten prices are the universal set \(\mathscr{E} = \{20, 21, 22, 23, 24, 25, 26, 27, 28, 29\}\). Set \(Y\) is the even prices, \(Y = \{x : x \text{ is even}, x \in \mathscr{E}\}\).
- List the members of \(Y\). (1)
- Give \(n(Y)\). (1)
- Give \(n(Y) + n(Y')\). (1)
Answer Details
Set-builder notation defines membership by a rule applied to every element of \(\mathscr{E}\); here "even" is checked against each price from 20p to 29p.
- The even prices from 20 to 29 are: \[Y = \{20, 22, 24, 26, 28\}\] [1]
- \(Y\) has five members, so \(n(Y) = 5\). [1]
- Since \(\mathscr{E}\) has ten prices in total, \(n(Y') = 10 - 5 = 5\), and \[n(Y) + n(Y') = 5 + 5 = 10\] which equals \(n(\mathscr{E})\), as it always must for any set and its complement. [1]
\(n(Y) + n(Y')\) always equals \(n(\mathscr{E})\) for any set \(Y\): together a set and its complement account for every element of the universal set exactly once.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning