Consider 3 turing machine each for A,B,C
from above problem it can be interpreted that any string w from $\sum_{ }^{*}$ can be accepted by exactly either A or B or C.
so
run these 3 turing mahine on string w parallely
as we are sure that exactly one of them will accept so whenever any one TM accept that w then can simply say the other will reject and halt them
ex- if w is accepted by TMa then we can halt TMb and TMc
it can be done for all the three TM's so A,B,C all the three are decidable