Set language and notation

Sample Set language and notation questions

A few of the 26 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 11 markGrade 3
   $P = \{1, 3, 5, 7, 9\}$ $Q = \{2, 4, 6, 8, 10\}$ Which of these is $P \cap Q$? [1]
   Show the worked solution

   No element is in both sets, so the intersection has no elements. It is the empty set, $\varnothing$. B1
2. Question 22 marksGrade 3-4
   $\xi = \{1, 2, 3, \ldots, 10\}$ $A = \{2, 3, 5, 7\}$
3. Question 31 markGrade 4-5
   The Venn diagram shows the sets $A$ and $B$. The four regions are labelled i, ii, iii and iv. Which region represents $A' \cap B$? [1]
4. Question 43 marksGrade 4
   The Venn diagram shows the numbers of elements in the regions of two sets, $A$ and $B$. (a) Find $n(A \cap B)$. [1] (b) Find $n(A \cup B)$
5. Question 52 marksGrade 5
   $B = \{(x, y): y = 3x - 2\}$ (a) The point $(4, k)$
6. Question 62 marksGrade 6
   $A = \{(x, y): y = x + 3\}$ $B = \{(x, y): y = 2x - 1\}$

Common mistakes in Set language and notation

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Swaps x and y in ordered pair

  Wrote the coordinates the wrong way round. The point is (x, y), with x first.

• Adds without subtracting overlap

  Added n(B) and n(S) without subtracting the 8 elements counted twice in the overlap.

• Empty set is zero

  The set {0} has one element (the number 0). The empty set ∅ has no elements at all.