Equal sets

Two sets A and B are equal sets when they have the same elements. To indicate two equal sets we write $$ A = B $$ To indicate two unequal sets we write $$ A \ne B $$

The order of the elements is irrelevant.

Example 1

Sets A and B are equal sets

$$ A = \{ 1,3,5,7 \} $$

$$ B = \{ 5,1,7,3 \} $$

Each element of set A is in set B. Each element of set B is in set A

Example 2

Sets A and C are not equal sets.

$$ A = \{ 1,3,5,7 \} $$

$$ C = \{ 5,1,7,4 \} $$

The element 3 is in the set A but not in the set C. The element 4 is in C but not in A.