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Corollary: Equality of Sets

Two sets $A$ and $B$ are considered equal, if $A$ is a subset of $B$, and vice versa. Formally:

$$A=B\Longleftrightarrow (A\subseteq B)\wedge (B\subseteq A).$$

The negation of the equality of sets is their inequality and denoted by $A\neq B.$

Examples

  1. The set of all animals and the set of all whales are not equal since every whale is an animal but not every animal is a whale.
  2. The set of all whole numbers $a\ge 0 $ equals the set $\mathbb N$ of all natural numbers.
  3. The sets $\{3,6,7\}$ equals the set $\{7,3,6\}.$

| | | | | created: 2017-08-13 11:44:27 | modified: 2020-05-10 18:35:44 | by: bookofproofs | references: [711]

1.Proof: (related to "Equality of Sets")

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[711] Mendelson Elliott: “Theory and Problems of Boolean Algebra and Switching Circuits”, McGraw-Hill Book Company, 1982