Venn Diagrams and Set Notation - Worksheets, Questions and Revision

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KS3 · Probability

KS3.M-P6 Venn Diagrams and Set Notation

AQA KS3.M-P6 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the meaning of each set notation.
(a)A n B(1)
(b)A u B(1)
(c)A' (the complement of A, within the universal set U)(1)
2
In a group of 50 pupils, 30 study French and 22 study German. If 10 study both French and German, how many pupils study at least one of French or German?
(2)
3
Complete the two-set Venn diagram. There are 40 people. 18 are in A, 15 are in B and 7 are in neither. Fill the three regions: A only, B only, and A n B.
(a)A n B (both)(1)
(b)A only(1)
(c)B only(1)
4
Use inclusion-exclusion. In a class of 28, 12 read book A and 9 read book B. Work out how many read neither if 4 read both.
(2)
5
If U is the universal set and A is a subset of U, what is A u A'? State the result.
(1)
6
In a club of 80 members, 50 like tea, 30 like coffee and 10 like both. What is the probability that a randomly chosen member likes tea or coffee or both? Give your answer as a fraction in simplest form.
(2)
7
Three-set Venn. In a group of 60, 30 are in A, 25 in B, 20 in C. Exactly 5 are in all three sets. There are 10 in both A and B, 8 in both A and C and 6 in both B and C (these pairwise numbers include the 5 who are in all three). Fill in the number of elements in each of the seven non-overlapping regions: (A only), (B only), (C only), (A and B only), (A and C only), (B and C only), (A and B and C).
(a)A and B and C (all three)(1)
(b)A and B only (in A and B but not C)(1)
(c)A and C only (in A and C but not B)(1)
(d)B and C only (in B and C but not A)(1)
(e)A only(1)
(f)B only(1)
(g)C only(1)
Mark scheme · KS3.M-P6 Venn Diagrams and Set Notation

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7