In a school, 100 students have access to three software packages, A, B and C 28 did not use any software 8 used only packages A 26 used only packages B 7 used only packages C 10 used all three packages 13 used both A and B (1) Draw a Venn diagram with all sets enumerated as for as possible. Label the two subsets which cannot be enumerated as x and y, in any order. ii) If twice as many students used package B as package A, write down a pair of simultaneous equations in x and y. i) Solve these equations to find x and y.

In a school, 100 students have access to three software packages, A, B and C 28 did not use any software 8 used only packages A 26 used only packages B 7 used only packages C 10 used all three packages 13 used both A and B (1) Draw a Venn diagram with all sets enumerated as for as possible. Label the two subsets which cannot be enumerated as x and y, in any order. ii) If twice as many students used package B as package A, write down a pair of simultaneous equations in x and y. i) Solve these equations to find x and y.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

perform your work on paper and submit through file
In a school, 100 students have access to three software packages,
A, B and C
28 did not use any software
8 used only packages A
26 used only packages B
7 used only packages C
10 used all three packages
13 used both A and B
(i)
Draw a Venn diagram with all sets enumerated as for as possible.
Label the two subsets which cannot be enumerated as x and y, in any
order.
(ii)
If twice as many students used package B as package A, write down a
pair of simultaneous equations in x and y.
Solve these equations to find x and y.
How many students used package C?
(iii)
(iv)

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