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Grade 9

1.09 Language and notation of sets

Worksheet
Set notation
1

List all the elements in the following sets:

a

{\{x|x \text{ is a positive even integers that are less than }16}\}

b

{\{x|x \text{ is an integer between} -8 \text{ and} -3 \text{ (not inclusive)}}\}

c

{\{x|x \text{ is an odd whole number less than } 13}\}

d

{\{x|x \text{ is a whole number between (and including) } 3 \text{ and } 7}\}

e
{\{x|x \text{ is a triangular number between } 0 \text{ and } 7}\}
f

\left\{1, \dfrac{1}{10}, \dfrac{1}{100}, \ldots, \dfrac{1}{100\,000}\right\}

g

\left\{2, 4, 8, \ldots, 64\right\}

2

Consider the following sets:

A = \left\{1, 2, 4, 8, 16\right\}, \quad B = \left\{1, 2, 4, 8\right\}

List all the elements in:

a
A \text{ or } B
b
Both A and B
3

Consider the set A = \left\{2, 4, 6, 8\right\}. Construct set builder notation for A.

4

Consider the following sets:

A = \left\{3, 6, 9, 12, 15, 18\right\}, B = \left\{3, 9, 12, 18\right\}, C = \left\{9, 18\right\}, \text{and } D = \left\{3, 6, 9, 12, 15, 18, 21\right\}

Determine whether the following statements is true or false:

a

B \subseteq D

b

C\subseteq B

c

B \subseteq C

d

\emptyset \subseteq B

5

Write \subseteq or \nsubseteq to make each of the following statements true:

a

\left\{1, 7, 9\right\} ⬚ \left\{0, 1, 3, 7, 9\right\}

b

\left\{0, 4\right\}⬚\left\{0, 3, 4, 5, 7\right\}

c

\left\{4, 5, 7\right\}⬚\left\{0, 3, 4, 7, 9\right\}

d

\left\{0, 1, 5\right\}⬚\left\{0, 1, 3, 7\right\}

6

Write \in or \notin to make each of the following statements true:

a

5 \ ⬚ \left\{2, 5, 6, 9\right\}

b

11\ ⬚\left\{4, 8, 12, 14\right\}

7

Consider the following sets:

  • A= \{ \text{letters of the word 'trapezium'}\}
  • B= \{ \text{letters of the word 'retire'}\}
  • C= \{ \text{letters of the word 'zapped'}\}
a

State the set of elements contained in both A and B.

b

Is B a proper subset of A?

c

State the set of elements contained in A or C

Operations on sets
8

Explain the meaning of the following statements:

a

Complement of set A.

b

Union of set A and set B.

c

Intersection of set A and set B.

d

Difference of two sets A and B.

9

P and Q are sets of vegetable types:

P= \{carrots, cauliflowers, beans\}; Q = \{cauliflowers, potatoes\}

There are no other vegetable types in universal set U.

a

Is P \cup Q the set of all vegetable types?

b

List the elements in the set P \cap Q.

10

P and Q are sets of flower varieties:

P= \{roses, lillies, daisies\}; Q= \{lillies, sunflowers\}

There are no other flower varieties in universal set U.

List the elements in the following sets:

a
Q'
b
Q \cap P
c
Q \cup P
d
Q' \cap P
11

The sets U = \left\{20, 8, 26, 3, 15\right\} and V = \left\{20, 8, 26, 3, 15, 2, 24, 10, 27\right\} are such that there are no other elements outside of these two sets.

a

Is U a proper subset of V?

b

State the cardinality of U.

c

List the elements of U'.

d

List the elements of the universal set.

e

Find V'.

12

Consider the following sets:

A = \left\{1, 2, 3, 4, 5, 6, 7\right\},B = \left\{1, 2, 3, 4\right\}

If there are no elements contained outside of these sets, find:

a
B'
b
A'
13

Consider the following sets:

\\

A = \{ \text{people who like football} \}

B = \{ \text{people who like softball} \}

C = \{ \text{people who like swimming} \}

D = \{ \text{people who do not like any of these} \}

a

Describe set B'.

b

Describe set D'.

14

Suppose set A = \left\{3, 4, 5, 6, 7\right\} and set B = \left\{3, 7, 8, 9\right\}. Find A \cap B.

15

List the elements of A \cap B given the following sets:

a

A= \{ \text{even numbers} \} and B = \{ \text{square numbers less than}\text{ } 100 \}.

b

A= \{ \text{multiples of} \text{ } 5\} and B= \{ \text{positive numbers less than} \text{ } 50 \}

16

If A is the set of factors of 24, and B is the set of factors of 36, then list the elements of:

a

B \cup A

b

A \cap B

17

Set A is the set of possible outcomes from rolling a standard die, and set B is the set of possible outcomes from rolling an eight-sided die. List the elements of the following sets:

a

A

b

B

c

A \cap B

d

A \cup B

Venn diagrams
18

Consider the following Venn diagram:

a

Find the set A - B.

b

Find the set A - B'.

19

Consider the following Venn diagram:

a

Find the set A' - B.

b

Find the set (A - B)'.

20

Consider the following Venn diagram:

a

Is A a subset of B?

b

Is A a proper subset of B?

21

Consider the following diagram:

a

Find the set A \cap C.

b

Find the set \left(B \cap C\right) '.

c

Find the set A \cap B \cap C.

d

Find the set A \cap \left( B \cup C \right).

e

Find the set \left(A \cap B \right)\rq.

22

Consider the following Venn diagram:

a

Is (A \cap B)' equal to A'\cup B' for all sets?

b

Is A' \cap B' equal to A \cup B' for all sets?

23

Consider the following Venn diagram:

Find the elements in the following:

a

A \cap B' \cap C'

b

A \cap B \cap C'

c

A' \cap B \cap C'

d

A \cap B' \cap C

e

A \cap B \cap C

f

A' \cap B \cap C

g

A' \cap B' \cap C

h

A' \cap B' \cap C'

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Outcomes

9.B1.2

Describe how various subsets of a number system are defined, and describe similarities and differences between these subsets.

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