1.02 Venn diagrams and sets
Match each symbol with its meaning.
Empty set
Intersection (conjunction)
Union (disjunction)
Complete each statement.
B=\emptyset means that \emptyset is the only element of the set.
A=\left\{⬚\vert -\infty \lt x\leq 6\right\} means that A is the set of all x \, ⬚ -\infty \lt x \leq 6.
A=\left\{⬚: ⬚\right\} means that A is the set of all y such that -\infty \lt y \lt \infty or that ⬚ is any real number.
For each pair, determine if B \subset A, B \subseteq A, or neither.
A = \left\{5, 9, 14, 15, 22, 28\right\}
B = \left\{15, 9, 28, 5, 14\right\}
A = \left\{\text{red, blue, green, yellow}\right\}
B = \left\{\text{green, yellow, red, purple}\right\}
A = \left\{-2, -1, 0, 1, 2\right\}
B = \left\{-2, -1, 0, 1, 2\right\}
A = \text{the set of all integers}
B = \text{the set of all even whole numbers}
Determine the intersection (conjunction) for each pair:
A = \left\{0, 1, 4, 9, 16, 25, 36, 49\right\}
B = \left\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\right\}
P = \left\{1, 3, 5, 7, 9, 11, 13\right\}
Q = \left\{0, 2, 4, 6, 8, 10, 12\right\}
Determine the union (disjunction) of each pair:
A = \left\{9, 99, 999, 9999\right\}
B = \left\{0, 1, 99, 100, 101\right\}
J = \text{the set of multiples of 5}
K = \text{the set of multiples of 10}
Match each of the Venn diagrams to the correct statement.
A \cap B =\{\emptyset\}
B \cap A\rq has 12 elements
List the elements in each of the subsets:
In a survey, a group of students were asked about their siblings. The two categories show if they have at least one brother and if they have at least one sister:
Find the number of students that have:
At least one sibling.
At least one brother.
No sisters.
Let S represent the set students who have a sister. Let B represent the set students who have a brother. Use set notation to describe the region which contains the students who have:
No siblings.
A brother and a sister.
Only have a sister.
A brother or a sister, but not both.
June is struggling to decide what movie to watch online. A Venn diagram of her options sorts movies into three categories based on their genre: Comedy, Action and Horror.
She decides to pick one movie at random from the streaming website. What is the probability that she selects:
A horror movie?
A movie that only fits into one exactly genre?
A movie that fits into at least two genres?
A group of 60 people were surveyed on whether they enjoyed skateboard riding or bike riding.
16 people said they enjoyed skateboard riding but not bike riding
25 people said they enjoyed bike riding only
12 people said they enjoyed both activities
7 people said they did not enjoy either activity
Complete the Venn diagram with the given information.
Out of a group of 40 students, 12 of them enjoy singing but not dancing. 13 enjoy both singing and dancing, while 8 do not enjoy either activity.
Create a Venn diagram including the given information.
One student from the group is randomly selected. Determine the probability of:
The student enjoying dancing, but not singing.
The student enjoying singing.
The student enjoying singing or dancing.
Consider the Venn diagram:
Set P is given as A \cap B. Highlight set P on the diagram and determine its elements.
Set Q is given as A\rq \cap B. Highlight set Q on the diagram and state its elements.
Express the set P \cup Q in terms of A and B.
A group of people were asked about whether they liked watching basketball and/or baseball. The results are shown in the Venn diagram:
Eiichiro makes this claim:
"In total 70 people like watching basketball, and 63 people like watching baseball. When added to the 31 people who do not like watching either sport, this means that 164 people in total were surveyed."
Explain why Eiichiro's reasoning is incorrect, and fix his mistake(s).
A manager is assessing the participation of employees in two different training programs: leadership development and project management. Out of a team of 40 members, 32 attended the leadership development program and 15 attended the project management training.
Given that everyone in the team attended at least one training, find out how many employees attended both trainings.
Construct a Venn diagram that represents the given information.
100 students were asked whether they studied History or Geography.
Let H represent History, G represent Geography, and S represent the universal set. Select all correct statements.
S is the set of all polygons, A is the set of all triangle, B is the set of all non-triangles.
Are these statements true? Use a diagram to justify your answers.
Given a set A and a universal set S, determine an expression for \left( A\rq\right)\rq, the negation of the negation of A. Explain your answer.
Given any two sets A and B, determine which would be greater, P\left(A \cup B\right) or P\left(A \cap B\right). Explain your reasoning.
Draw a Venn diagram that meets the given criteria.
A \cap B = \emptyset
C \cap B \neq \emptyset
A \subset C
C\subset S