Linear Algebra Examples

$A = (1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19)$ , $b = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)$

Step 1

Set up the intersection notation of set ${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}$ and ${1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$ .

${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} \cap {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$

Step 2

The intersection of two sets is the set of elements which are in both sets.

${1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}$

Step 3

The complement of the two sets is the remaining members of ${1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}$ that aren't members of the intersection of the two sets.

${2, 4, 8, 10, 14, 16, 20}$