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The inverse relation

If R is a relation from A to B, then we can define a relation from

B to A, denoted by R -1, and cali it as the inverse relation of

the relation R: bR-\a <=>aRb.

R-1 = {(b, a): (a, b) O R}

If R is a binary relation on a finite set A, then the graph ofR-l

can be obtained from the graph of R by reversing the

directions

of all of the arcs.

Examples:

1.    The inverse of the subset relation R on the family S of

sets

is the superset relation (/?-l, 52):

VA,B £SBR-\A <=>ARB <=>A OB (B is superset ofA).

2.    Let R be the relation of logical equivalence on the set Stat(P)

of all statements.

Then, sińce A =B <=>B the relation R is its own inverse:

R = R-l.