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.

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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”.