Set difference
The difference of two sets \(A\) and \(B\), denoted as \(A \backslash B\), is the set of elements in \(A\) but not in \(B\). The symbol, \(A - B\) is also used to denote set difference.
Example 1: Let \(O = \{0, 1, 2, 3, 4, 5, 6, 7\}\) be the set of octal digits and \(B = \{0, 1 \}\) be the set of binary digits. Then:
\[O \backslash B = O - B = \{2, 3, 4 , 5, 6, 7\}.\]There are the elements in the set \(O\) but not in the set \(B\). The Venn diagram shown below illustrates the set difference:
The difference of the set, \(A - B,\) is the set containing all elements in \(A\) that are not in the set \(B.\)
To compute \(O\) \ \(B\), find elements that are common to \(O\) and \(B\), and remove them from \(O\). More formally,
\(A \backslash B = \{x \vert x \in A\) and \(x \notin B \}\)