Bisi's shop till groups every item sold today into the universal set \(\mathscr{E}\). Set \(F\) is the set of items that are fresh produce. Of the 70 items ...
Question 1 Report
Bisi's shop till groups every item sold today into the universal set \(\mathscr{E}\). Set \(F\) is the set of items that are fresh produce. Of the 70 items sold, the diagram below shows how many fall in each region.
- Write down \(n(F)\). (1)
- Write down \(n(F')\). (1)
- Write down \(n(F)\) as a fraction of \(n(\mathscr{E})\), in its simplest form. (1)
Answer Details
On a single-circle Venn diagram, the two regions shown make up the whole universal set; a fraction comparing \(n(F)\) to \(n(\mathscr{E})\) should be reduced to its simplest form by dividing by the highest common factor.
- The number of fresh-produce items inside the circle is 26, so \(n(F) = 26\). [1]
- The number outside the circle is 44, so \(n(F') = 44\); checking, \(26 + 44 = 70\), matching the total items sold. [1]
- Writing \(n(F)\) over \(n(\mathscr{E})\) and simplifying: \[\frac{26}{70} = \frac{13}{35}\] (dividing numerator and denominator by their highest common factor, 2). [1]
Check a simplified fraction by trying to divide again: since 13 and 35 share no common factor (13 is prime and does not divide 35), \(\frac{13}{35}\) cannot be reduced further.
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