Sets & Venn Diagrams · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Venn diagrams and tables for sets

Mathematics · Probability · ages 12-14
Name ______________________   Date ____________

  1. In a Venn diagram of A and B, what does the region outside both circles represent?

    • A ∪ B
    • A ∩ B
    • Neither A nor B: outside both circles

  2. True or false: A′ (the complement of A) includes everything in circle B that does not overlap with circle A.

    Circle one:   True   False

  3. Set A = {2, 4, 6, 8} and Set B = {4, 8, 10, 12}. Which numbers belong to A ∪ B (in either set)?

    • 4 and 8
    • 2, 4, 6, 8, 10, 12
    • 2 and 6
    • 10 and 12

  4. Set A = {1, 2, 3}. Set B = {3, 4, 5}. What is A ∩ B?

    • {3}
    • {1, 2, 3, 4, 5}
    • {}

  5. 40 people were surveyed about drinks. 22 like tea, 18 like coffee, and 9 like both. How many people like only tea (not coffee)?

    Answer: ______________

  6. A class of 30 students was asked about sports. 12 play soccer, 15 play basketball, and 5 play both. Using a two-way table, how many students play neither sport?

    Answer: ______________

  7. In a Venn diagram with circles A and B inside a box, which region is shaded to show A ∩ B?

    • Everything outside circle A
    • Only the overlap of A and B
    • Everything inside circle A or circle B
    • Only the part of A that does not overlap B

  8. Set A is students who play chess. Shading A′ on the Venn diagram means shading...

    • Everyone inside circle A
    • Everyone outside circle A
    • Only the overlap of A and B

  9. Set A is multiples of 2 from 1 to 12. Set B is multiples of 3 from 1 to 12. Which numbers belong in the overlapping middle region?

    • 6 and 12
    • 2, 3, 4, 6, 8, 9, 10, 12
    • All numbers from 1 to 12

  10. A survey of 50 pet owners found 28 have a dog, 21 have a cat, and 6 have neither pet. Using a two-way table, how many owners have both a dog and a cat?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Venn diagrams and tables for sets W1-mt_1YwOCMMwD8-s1

  1. Neither A nor B: outside both circles · Outside both circles means the thing belongs to neither set: that region is the complement of A ∪ B.
  2. True · A′ means everything outside A, so any part of B sitting outside A still counts as part of A′.
  3. 2, 4, 6, 8, 10, 12 · A ∪ B combines every number that appears in either circle, with no repeats.
  4. {3} · Only 3 appears in both sets, so the intersection is {3}.
  5. 13 · Only-tea drinkers are the tea fans minus the ones who also like coffee.
  6. 8 · Add soccer and basketball players, subtract the ones counted twice, then subtract that from the whole class.
  7. Only the overlap of A and B · A ∩ B means 'in A and in B', so only the overlap where the two circles cross is shaded.
  8. Everyone outside circle A · The complement A′ is everyone who is not in A, so you shade the space outside its circle.
  9. 6 and 12 · Only 6 and 12 are multiples of both 2 and 3, so they're the only numbers in the overlap.
  10. 5 · Owners with a dog or a cat equal the total minus 'neither'; comparing that to the dog-plus-cat total reveals the overlap.
Worksheet · LightMySky