Recognize Equal Sets

Introduction

• Objective: Learn to recognize equal sets.

Definition of Equal Sets

• Set A is equal to Set B if both contain the exact same elements.
  • Order and repetition of elements do not affect equality.
• Symbolized by the statement A = B.

Equal vs. Equivalent Sets

• Equal Sets:
  • Contain the same elements.
• Equivalent Sets:
  • Contain the same number of elements.
• If two sets are equal, they are also equivalent.
• If two sets are equivalent, they are not necessarily equal.

Examples

• Example 1:

  • Set {7, 6, 5, 4} is equal to Set {4, 5, 6, 7}.
  • Both sets contain exactly the same elements.
  • Order does not count; therefore, the statement is true.

• Example 2:

  • Set {1, 3, 5} is equal to Set {0, 1, 3, 5}.
  • The second set has an extra element (0) which the first set does not have.
  • They do not contain exactly the same elements.
  • Therefore, the sets are not equal, meaning the statement is false.

Conclusion

• To determine if sets are equal, ensure they have the same elements, without considering the order or repetition.