19.01 Language and notation of sets
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.
The following jar contains 7 red, 3 blue and 10 greed marbles:
If a marble is drawn out of the jar without looking, list all the possible colours that the marble might be.
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.
A card is selected from a standard deck of 52 cards shown below. How many colour outcomes are there in the sample space?
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}\}
{\{x|x \text{ is a whole number between (and including) } 3 \text{ and } 7}\}
\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\{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:
B \subseteq D
C\subseteq B
B \subseteq C
\emptyset \subseteq B
Write \subseteq or \nsubseteq to make each of the following statements true:
\left\{1, 7, 9\right\} ⬚ \left\{0, 1, 3, 7, 9\right\}
\left\{0, 4\right\}⬚\left\{0, 3, 4, 5, 7\right\}
\left\{4, 5, 7\right\}⬚\left\{0, 3, 4, 7, 9\right\}
\left\{0, 1, 5\right\}⬚\left\{0, 1, 3, 7\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:
- A= \{ \text{letters of the word 'trapezium'}\}
- B= \{ \text{letters of the word 'retire'}\}
- C= \{ \text{letters of the word 'zapped'}\}
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 following statements:
Complement of set A.
Union of set A and set B.
Intersection of set A and set B.
Difference of two sets A and 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.
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:
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.
Is U a proper subset of V?
State the cardinality of U.
List the elements of U'.
List the elements of the universal set.
Find V'.
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'.
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
Consider the following Venn diagram:
Find the set A \cap B.
Find the set A \cap B'.
Consider the following Venn diagram:
Find the set (A \cup B)'.
Find the set A' \cup B.
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'
In picking a random card from a standard pack, which two of the following four events share no common outcomes?
Event A: picking a black card
Event B: picking a king
Event C: picking a spade
Event D: picking a club
Determine whether the following pairs of events are complementary or not:
Event A: Selecting a positive number.
Event B: Selecting a negative number.
Event A: Drawing a red card from a standard deck of cards (no jokers).
Event B: Drawing a black card from a standard deck of cards (no jokers).
Event A: Drawing a club from a standard deck of cards (no jokers).
Event B: Drawing a spade from a standard deck of cards (no jokers).
Event A: Rolling a number greater than 3 on a die.
Event B: Rolling a number less than 3 on a die.
Describe P(A \cup B ) in the following events:
Event A: It will rain tomorrow.
Event B: There will be a storm tomorrow.
Event A: Getting an odd number when a die is rolled
Event B: Getting a multiple of 3 when a die is rolled
Event A: Getting a black card
Event B: Getting a face card
Consider the following events:
-
Event A: Paul wins the golf tournament
Event B: Paul wins the badminton tournament
Write the notation that represents the probability that Paul wins either the golf or badminton but not both.
Write down three different notations for the probability of the following events:
Event A: getting a heads when a coin is tossed.
Event A: getting a number greater than 3 when a die is rolled.
Event A: getting a sum greater than 11 when two dice are rolled.
Event A: a baby born being a girl.
Event A: a card randomly selected from a deck being a club.
In an experiment, there are only two possible outcomes, A and B. If outcome A occurs, outcome B does not occur and vice versa.
Determine whether the following are true:
In an experiment, a number is chosen randomly from the numbers listed below:
2, \, 3, \, 5, \, 6, \, 7, \, 10, \, 12, \, 14, \, 15, \, 16, \, 19, \, 20
Consider the following events:
Event A: odd number is chosen
Event B: multiple of 4 is chosen
Find the following sets:
Which of the sets from part (a) has the largest probability.
Find: