3. A class of 28 students were surveyed and asked if they ever had a dog or cat as a pet. 18 students said they had a dog. 16 students said they had a cat. 4 students said they had never had a dog or a cat.
(i) Draw a Venn diagram to represent this information. (ii) How many students had both a cat and a dog? (iii) How many students had just one pet?
(iv) What percentage of the students surveyed did not have a pet? Give your answer to the nearest whole number.
4. In a school of 320 students, 85 students have visited France, 200 have visited Spain and 60 students have visited both countries.
(i) Draw a Venn diagram to represent this information. (ii) How many students have not visited either country? (iii) How many students have visited France only? (iv) What percentage of the students have visited Spain? (v)
If a student was picked at random from this group, what is the probability they have visited France or Spain, but not both countries?
5. Of 100 people in a summer camp, 70 members said they play a sport and 25 members take music lessons. 5 members do neither of these.
(i) Draw a Venn diagram to represent this information. (ii) How many members play a sport or take music lessons?
(iii) If you were to pick a member at random, what is the probability they take music lessons and play sport?
6. A market researcher collecting data from a certain number of households found that 81% have a smart TV, 60% have high-speed broadband and 56% have both.
(i) Draw a Venn diagram to represent this information. (ii) What percentage of households have a smart TV only? (iii) What percentage of people have neither a smart TV nor high-speed broadband?
(iv) If 200 households were surveyed in total, how many households does your percentage in part (iii) represent?
24.3 Further operations used with set notation
By the end of this section you should understand:
● set diff erence and the complement of a set and be able to solve problems
The diff erence (subtraction) of two sets can be explained as follows. The set A less the set B consists of elements that are in A but not in B. Mathematically, we write A less B as A\B.
The difference between two sets A and B is written as A\B. This is the set of elements which are contained in A but not in B.
A B A B
A\B is the red shaded area in the diagram. 394 Linking Thinking 1