Venn diagrams worksheets with answers

Cambridge IGCSE 0580

Use set notation to find intersections, unions and complements, and count the members of a set.

Sample sheet

Venn diagrams, Standard

Name Date

1
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$ $A = \{6, 9, 12\}$ $B = \{2, 3, 4, 6, 10, 12\}$ List the elements of $A' \cap B$ .
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2
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$ $A = \{1, 2, 3, 4, 5, 6, 7\}$ $B = \{1, 3, 5, 7, 9, 11, 13, 15\}$ List the elements $x$ for which $x \in A$ and $x \in B'$ .
[3]
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3
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{1, 2, 4, 5, 6, 7, 13, 14\}$ $B = \{1, 12, 14\}$ List the elements $x$ for which $x \in A$ and $x \in B'$ .
[3]
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4
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$ $A = \{2, 4, 6, 8, 11\}$ $B = \{3, 4, 9, 12\}$ List the elements of $(A \cup B)'$ .
[3]
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5
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{2, 7, 8, 10, 12\}$ $B = \{1, 5, 8, 11\}$ List the elements of $(A \cap B)'$ .
[3]
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6
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{3, 6, 9, 12\}$ $B = \{1, 4, 9\}$ Find $n(A')$ .
[3]
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Answers

Venn diagrams, Standard

1 $\{2, 3, 4, 10\}$
2 $\{2, 4, 6\}$
3 $\{2, 4, 5, 6, 7, 13\}$
4 $\{1, 5, 7, 10, 13\}$
5 $\{1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14\}$
6 $10$

Method in brief

The intersection holds the elements in both sets, the union holds the elements in either, and the complement holds the elements of the universal set that are not in the set. List each element once.

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More worksheets

Venn diagrams worksheets with answers

Cambridge IGCSE 0580

Use set notation to find intersections, unions and complements, and count the members of a set.

Sample sheet

Venn diagrams, Standard

Name Date

1
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$ $A = \{6, 9, 12\}$ $B = \{2, 3, 4, 6, 10, 12\}$ List the elements of $A' \cap B$ .
[3]
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2
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$ $A = \{1, 2, 3, 4, 5, 6, 7\}$ $B = \{1, 3, 5, 7, 9, 11, 13, 15\}$ List the elements $x$ for which $x \in A$ and $x \in B'$ .
[3]
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3
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{1, 2, 4, 5, 6, 7, 13, 14\}$ $B = \{1, 12, 14\}$ List the elements $x$ for which $x \in A$ and $x \in B'$ .
[3]
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4
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$ $A = \{2, 4, 6, 8, 11\}$ $B = \{3, 4, 9, 12\}$ List the elements of $(A \cup B)'$ .
[3]
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5
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{2, 7, 8, 10, 12\}$ $B = \{1, 5, 8, 11\}$ List the elements of $(A \cap B)'$ .
[3]
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6
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$ $A = \{3, 6, 9, 12\}$ $B = \{1, 4, 9\}$ Find $n(A')$ .
[3]
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Answers

Venn diagrams, Standard

1 $\{2, 3, 4, 10\}$
2 $\{2, 4, 6\}$
3 $\{2, 4, 5, 6, 7, 13\}$
4 $\{1, 5, 7, 10, 13\}$
5 $\{1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14\}$
6 $10$

Method in brief

The intersection holds the elements in both sets, the union holds the elements in either, and the complement holds the elements of the universal set that are not in the set. List each element once.

Learn the method

Stuck on a question?

Scan the code beside a question to get help with it.

Open the tutor