#Type/Definition #Topic/Linear_Algebra

Types: N/A
Examples: 1.10 Proving Set Equality
Constructions: N/A
Generalizations: 1.7 Subset

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Set Equality

Sets A and B are equal, denoted A=B, if and only if:

  1. A⊆B
  2. B⊆A

Note that the = sign is a nonnumeric equal sign.

Direct of Proof A=B

To show sets A and B are equal, we:

  1. Show A⊆B
  2. Show B⊆A
  3. Conclude A=B by definition (mic drop!)