Definition·D019
Converse relation
The relation read backwards: all pairs flipped.
for a relation
from
to
, so that
.
In words
The converse of R is the set of pairs p in the product of B and A for which there are a and b with p the reversed pair of b then a and the pair of a and b in R, so that b is related to a in the converse exactly when a was related to b originally.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
Exists by Separation inside
(product, ordered pairs). For a general relation the converse is just another relation; the interesting case is a bijective function, whose converse is again a function, the inverse function, written with the same symbol
: that is L03.