Section 1.1 & 1.2: Types of Relations

Show that the relation \(R\) in the set \(A = \{1, 2, 3, 4, 5\}\) given by
\[R = \{(a, b) : |a - b| \text{ is even}\}\]
is an equivalence relation. Show that all the elements of \(\{1, 3, 5\}\) are related to each other and all the elements of \(\{2, 4\}\) are related to each other. But no element of \(\{1, 3, 5\}\) is related to any element of \(\{2, 4\}\).