List all the possible outcomes when a coin is flipped.
A standard six-sided die is rolled.
List the sample space.
List the sample space for rolling a number strictly less than 3.
List the sample space for rolling a number divisible by 3.
List the sample space for rolling an even number.
Uther rolled a standard six-sided die.
List all the numbers that the die may land on.
Uther rolled a number less than 3. List all the numbers that he could have rolled.
List all the elements in the following sets:
{\{x:x \text{ is a positive even integers that are less than }16}\}
{\{x:x \text{ is an integer between} -8 \text{ and} -3 \text{ (not inclusive)}}\}
{\{x:x \text{ is an odd whole number less than } 13}\}
\left\{1, \dfrac{1}{10}, \dfrac{1}{100}, \ldots, \dfrac{1}{100\,000}\right\}
\left\{2, 4, 8, \ldots, 64\right\}
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:
Consider the set A = \left\{2, 4, 6, 8\right\}. Construct set builder notation for A.
Consider the following sets:
A = \left\{8, 12, 16, 20, 24, 28\right\}, B = \left\{8, 12, 16, 28\right\}, C = \left\{12, 16\right\}, \text{and } D = \left\{4, 8, 12, 16, 20, 24, 28\right\}
Determine whether the following statements are true or false:
B \subset D
C\subset B
A \subset B
\emptyset \subset D
Write \subseteq or \nsubseteq to make each of the following statements true:
\left\{1, 2, 4\right\} ⬚ \left\{1, 2, 4, 7, 8\right\}
\left\{8, 9\right\} ⬚ \left\{3, 4, 7, 8, 9\right\}
\left\{3, 4, 9\right\} ⬚ \left\{2, 4, 7, 8, 9\right\}
\left\{1, 3, 8\right\} ⬚ \left\{1, 4, 7, 8\right\}
Write \in or \notin to make each of the following statements true:
5 \ ⬚ \left\{2, 5, 6, 9\right\}
11\ ⬚\left\{4, 8, 12, 14\right\}
Consider the following sets:
State the set of elements contained in both A and B.
Is B a proper subset of A?
State the set of elements contained in A or C.
Explain the meaning of "the complement of set A."
A set is defined as A=\left\{ x:0\leq x \leq 5 \text{ and }x \text{ is an integer} \right\}.
List the elements of set A.
Is set B=\left\{2, 3, 5\right\} a subset of set A?
Consider the sets A=\left\{ x:-6\lt x \lt 6 \text{ and }x \text{ is an integer} \right\} and \\ B=\left\{ x:-1\leq x \leq 10 \text{ and }x \text{ is an integer} \right\}.
Find n(A).
Find n(B).
Find n(A \cap B).
Find n(A \cup B).
State whether the following points are in the set A=\left\{(x, y) : y = 5x-7 \right\}:
Consider the sets A=\left\{(x, y) : y = 3x-4 \right\} and B=\left\{(x, y) : y = 2x+6 \right\}.
Explain why n(A \cap B)=1.
Find A \cap B.
Explain the meaning of the following statements:
Union of set A and set B.
Intersection of set A and set B.
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.
Is P \cup Q the set of all vegetable types?
List the elements in the set P \cap Q.
Suppose set A = \left\{3, 4, 5, 6, 7\right\} and set B = \left\{3, 7, 8, 9\right\}. Find A \cap B.
List the elements of A \cap B given the following sets:
A= \{ \text{even numbers} \} and B = \{ \text{square numbers less than}\text{ } 100 \}.
A= \{ \text{multiples of} \text{ } 5\} and B= \{ \text{positive numbers less than} \text{ } 50 \}
If A is the set of factors of 24, and B is the set of factors of 36, then list the elements of:
B \cup A
A \cap B
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
B
A \cap B
A \cup B
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:
Is \left(P \cup Q\right) \rq empty?
The sets V = \left\{21, 8, 30, 9, 28\right\} and W = \left\{21, 8, 30, 9, 28, 7, 13, 12, 26\right\} are such that there are no other elements outside of these two sets.
Is V a proper subset of W?
State n\left(V\right), the order of V.
List the elements of V'.
List the elements of the universal set.
Find W'.
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:
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} \}
Describe set B'.
Describe set D'.
Consider the sets A=\left\{ x:-7\leq x \leq 10 \text{ and }x \text{ is an integer} \right\}, B=\left\{-2, 4, 8\right\} and \\ C=\left\{3, -5, 11\right\}.
Is set B a subset of set A?
Is set C a subset of set A?
List the elements in the set A \cap C.
List the elements in the set A' \cap C.
Find n \left( A \cup C \right).
Find n \left( A \cap C' \right).
For each of the following, identify the Venn diagram that best represents the sets A and B:
Venn diagram 1
Venn diagram 3
Venn diagram 2
Venn diagram 4
A = \left\{\text{Earth}\right\}, B = \left\{\text{Planets}\right\}
A = \left\{6, 8, 4, 2, 7\right\}, B = \left\{3, 6, 1\right\}
A = \left\{\text{w}, \text{i}, \text{n}, \text{d}\right\}, B = \left\{\text{e}, \text{a}, \text{r}, \text{t}, \text{h}\right\}
A = \left\{\text{Animals found in Australia}\right\}, B = \left\{\text{Animals found in NSW}\right\}
We are interested in the colour of a card randomly drawn from a standard deck. Draw a Venn diagram to illustrates this.
Consider the Venn diagram:
List the elements in:
A \cap B
A \cup B
Consider the Venn diagram:
List the elements in:
A \rq
B \rq
Consider the Venn diagram:
List the elements in:
A
U
B \rq
Consider the Venn diagram:
List the elements in:
A \cap B \rq
\left(A \cup B\right) \rq
Consider the following Venn diagram:
Is A a subset of B?
Is A a proper subset of B?
Consider the following diagram:
Find the set A \cap C.
Find the set \left(B \cap C\right) '.
Find the set A \cap B \cap C.
Find the set A \cap \left( B \cup C \right).
Find the set \left(A \cap B \right)\rq.
Consider the following Venn diagram:
Is (A \cap B)' equal to A'\cup B' for all sets?
Is A' \cap B' equal to A \cup B' for all sets?
Consider the following Venn diagram:
Find the elements in the following:
A \cap B' \cap C'
A \cap B \cap C'
A' \cap B \cap C'
A \cap B' \cap C
A \cap B \cap C
A' \cap B \cap C
A' \cap B' \cap C
A' \cap B' \cap C'
The Venn diagram shows the number of students in a school playing Rugby League (L), Rugby Union (U), both or neither.
Complete the table of values below:
Play Rugby League | Don't play Rugby League | |
---|---|---|
Play Rugby Union | ||
Don't play Rugby Union |
Find the following:
n(L\cap{U}')
n(L)
n(U)
n(U\cap L')
n({L}')
n({U}')