Grade DE Venn diagrams Enumerate sets and combinations

Grade D/E Venn diagrams Enumerate sets and combinations of sets systematically, using Venn diagrams If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Venn diagram

Example 1 100 people are asked if they like watching football on television and if they like watching rugby on television. 77 like watching football and 42 like watching rugby. 8 people liked neither. Complete a Venn diagram to show this information.

Solution to example 1 100 people are asked if they like watching football on television and if they like watching rugby on television. 77 like watching football and 42 like watching rugby. 8 people liked neither. 100 – 8 = 92 77 + 42 – 92 = 27 42 – 27 = 15 77 – 27 = 50 Complete a Venn diagram to show this information. ξ Like football 50 8 Like rugby 27 15

Example 2 • ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} • A = {multiples of 5} • B = {even numbers} • Draw a Venn diagram for this information.

Solution to example 2 A B 2 5 4 10 8 6 1 3 7 9

Now try these…… 1. 50 people are asked about what food they like. 42 like yoghurt, 30 like cereal, 3 like neither. Draw a Venn diagram to show this information. 2. ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {multiples of 3} B = {odd numbers} Draw a Venn diagram for this information

Solution to question 1 50 – 3 = 47 42 + 30 – 47 = 25 42 – 25 = 17 Cereal Yoghurt 17 3 30 – 25 = 5 25 5

Solution to question 2 B A 6 12 2 4 8 10 3 1 5 9 7 11

Problem solving and reasoning (a) Write down the numbers that are in set S ∪ B (b) Write down the numbers that are in set S ∩ B One of the numbers in the diagram is chosen at random. (c) Find the probability that the number is in set Bʹ.

Problem solving and reasoning solution •