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 - B.
Find the set A - B'.
Consider the following Venn diagram:
Find the set A' - B.
Find the set (A - 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'
