2.3.2 Venn diagrams and set notation

• What is a set in mathematical terms?

  A collection of distinct objects
• An empty set contains no elements.
• If A \subseteq B</latex> and $A \neq B$, then A is a proper
• What is the universal set denoted as?

  $\mathbb{U}$
• If $A =$$\{1, 2\}$ and $B =$$\{1, 2, 3\}$, then $A \subset B$.
• Match the Venn diagram element with its description:

  Circles ↔️ Represent individual sets

  Overlapping Regions ↔️ Represent the intersection of sets

  Universal Set ↔️ Contains all relevant elements
• The overlapping regions in a Venn diagram represent the intersection
• In a Venn diagram, what do regions outside the circles but within the universal set represent?

  Elements not in the sets
• Steps to create a Venn diagram for two sets A and B

  1️⃣ Draw the universal set as a rectangle

  2️⃣ Draw circles for sets A and B within the universal set

  3️⃣ Fill in the overlapping region with elements common to both A and B

  4️⃣ Fill in the regions in A and B with their unique elements

  5️⃣ Place elements outside the circles but within the rectangle
• What does the region 'A only' in a Venn diagram for two sets A and B represent?

  Elements in A but not B
• In a Venn diagram, the universal set is represented by a rectangle
• What do the regions within the circles in a Venn diagram represent?

  Sets
• Regions outside the circles in a Venn diagram represent elements not in the sets
• In a Venn diagram, the region labeled "A only" contains elements in A but not in B.
• What does the universal set in a Venn diagram contain?

  All possible elements
• Overlapping regions in a Venn diagram indicate the intersection
• Match the region in a Venn diagram with its description:

  A only ↔️ Elements in A but not B

  B only ↔️ Elements in B but not A

  A ∩ B ↔️ Elements in both A and B
• What shape represents the universal set in a Venn diagram?

  Rectangle
• The overlapping regions in a Venn diagram are called intersections.
• Regions outside both circles in a Venn diagram represent elements in neither A nor B.
• What does $A \cap B$ represent in set notation?


  Intersection
• A set is a collection of distinct objects called elements.
• The universal set contains all possible elements relevant to a context
• What is another name for the empty set?

  Null set
• An element is an object that belongs to a set
• What symbol is used to represent the empty set?

  $\emptyset$
• A proper subset of B cannot be equal to B.
• What is a set in mathematical terms?

  A collection of distinct objects
• A set is typically denoted with capital letters.
• The universal set contains all possible elements relevant to a specific context.
• If studying numbers less than 10, the universal set is \{1, 2, 3, 4, 5, 6, 7, 8, 9\}.
• An empty set contains no elements.
• Give an example of an empty set.

  Even prime numbers greater than100
• If A \subseteq B</latex> and $A \neq B$, then A is a proper subset of B.
• If $A =$$\{1, 2\}$ and $B =$$\{1, 2, 3\}$, then $A \subseteq B$ is true.
• What is the purpose of a Venn diagram?

  To show relationships between sets
• In a Venn diagram, the universal set is represented by a rectangle.
• The overlapping region in a Venn diagram represents the intersection of sets.
• What does the notation $A \cup B$ represent?


  Union of A and B
• The intersection $A \cap B$ includes elements common to both A and B.