A close examination of this particular circuit will reveal
that when input "A" goes high it not only presents
a request at the input of U2A, but it also presents a disable
to U1A and U4A. This also causes a "Cascading Series of
Disables" to U1B, U4B, and U2B, which would prevent "X"
or "Y" or "Z" from becoming active. Providing
that there are no high inputs at "B" or "C"
or "D", U2A is enabled to be driven low at the output.
This simple principle of "Disabling" all to the
left or to the right of the selected input, is what provides
for the "Exclusive-OR" action, in that ANY one, but
ONLY one will activate the outputs. Providing more than one active
input will disable each other.