"Membership and cardinality of sets"

Overview of Sets and Cardinality

• Sets Definition: A set is a collection of distinct objects, considered as an object in its own right.

• Membership: The elements of a set are referred to as its members. The membership can be expressed as:

  • p \, \in \, S means "p is an element of S".
  • p \, \notin \, S means "p is not an element of S".

Example Sets

• Set A: The set of integers greater than or equal to -7 and less than or equal to -1.

  • Elements of Set A: A = {-7, -6, -5, -4, -3, -2, -1}
  • Cardinality of Set A: n(A) = 7

• Set B: The set of integers greater than or equal to -29 and less than or equal to 30.

  • Elements of Set B: B = {-29, -27, -22, 24, 27, 30}
  • Cardinality of Set B: n(B) = 6

Determining Cardinality

• To find the cardinality of a set:
  • List all elements of the set.
  • Count the distinct elements to obtain the cardinality.

Membership Questions

• Analyze the following membership statements for Sets A and B:

  • Statement: "24 \, \in \, B"

  • Answer: True

  • Statement: "-12 \, \in \, A"

  • Answer: False

  • Statement: "-25 \, \notin \, B"

  • Answer: True

  • Statement: "-6 \, \in \, A"

  • Answer: True

Key Takeaways

• Cardinality is a measure of the number of distinct elements within a set.
• Understanding the notation for set membership is essential for working with sets and their elements.
• Practice identifying elements within sets to improve accuracy with membership questions.