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Venn diagrams – practice for Years 3–8

Sample questions on Venn diagrams with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Logic
Year
Years 3–8
Curriculum area
Deduction

Question types: Sets of children

Rule: Venn diagrams

The overlap holds the children who are in both A and B. Those only in A or only in B are in exactly one set.

All children = only A + only B + both + neither. A + B counts the overlap twice.

Example: 20 children, 12 in A, 10 in B, none outside: 12 + 10 − 20 = 2 are in both.

Watch out: Set A includes the children in the overlap too: A = only A + both.

Sample questions

  1. Question 1 Easy

    A is the children who have a dog, B the children who have a cat. How many children are in set A?

    AB11911
    Show the solution
    Answer: 20

    How it works: 11 + 9 = 20

  2. Question 2 Normal

    A is the children who have a dog, B the children who have a cat. There are 38 children in the class. How many of them are in neither A nor B?

    AB11911?
    Show the solution
    Answer: 7

    How it works: 38 − 11 − 9 − 11 = 7

  3. Question 3 Hard

    A is the children who have a dog, B the children who have a cat. There are 38 children in the class, 20 in set A and 20 in set B. How many children are in both sets?

    AB?7
    Show the solution
    Answer: 9

    How it works: 20 + 20 − (38 − 7) = 9

Related topics

All Logic topics

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