Define the term of Inverse of a relation.
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Define the term of Inverse of a relation.
Define the term of Inverse of a relation.
For any binary relation R, a second relation can be constructed by merely interchanging first and second components in every ordered pair.
The relation thus obtained is called the inverse of the first one and designated as R–1.
Thus, R–1 = {(y, x) : (x, y) ∈ R}
For example,
1. Then inverse of the husband-wife relation is wife-husband relation.
2. Let R = {(2, 1), (3, 2), (4, 3), (4, 5)}. Then,
R–1 {(1, 2), (2, 3), (3, 4), (5, 4)}.
So (R–1)–1 = R.