A1:
rng (R \/ S) = (rng R) \/ (rng S)
by RELAT_1:12;

( rng R c= X & rng S c= X ) by RELAT_1:def 19;

hence rng (R \/ S) c= X by A1, XBOOLE_1:8; :: according to RELAT_1:def 19 :: thesis: verum

( rng R c= X & rng S c= X ) by RELAT_1:def 19;

hence rng (R \/ S) c= X by A1, XBOOLE_1:8; :: according to RELAT_1:def 19 :: thesis: verum