Set Difference/Examples

Examples of Set Difference

Example: $\set {1, 2, 3} \setminus \set { 2, 4, 5, 6}$

Let $S$ and $T$ be sets such that:

$S = \set {1, 2, 3}$

$T = \set {2, 4, 5, 6}$

Let $\setminus$ denote set difference.

Then:

$S \setminus T = \set {1, 3}$

while:

$T \setminus S = \set {4, 5, 6}$

Arbitrary Example $1$

Let:

\(\ds A\)

\(=\)

\(\ds \set {1, 2}\)

\(\ds B\)

\(=\)

\(\ds \set {2, 3}\)

Then:

$A \setminus B = \set 1$

Arbitrary Example $2$

Let $S$ and $T$ be sets such that:

$A = \set {1, 2, 3}$

$B = \set {1, 2, 4, 5}$

Let $\setminus$ denote set difference.

Then:

$A \setminus B = \set 3$