$Version
(* "13.1.0 for Mac OS X x86 (64-bit) (June 16, 2022)" *)
Clear["Global`*"]
f1 = Sin[x y]; f2 = x + y; f3 = x + z;
data1 = Transpose[{
(Rest@
Subsets[
{f1 < 1/8, f2 < 1/2, f3 < 1/2},
3]),
Rest@
Subsets[
Opacity[0.5, ColorData[97][#]] & /@
Range[3],
3]}];
data2 = ReplacePart[#, 1 -> And @@ #[[1]]] & /@ data1;
data = Drop[Riffle[data1, data2], {1, 5, 2}];
Partition[
Insert[RegionPlot3D[Evaluate@#[[1]],
{x, 0, 1}, {y, 0, 1}, {z, 0, 1},
PlotStyle -> #[[2]],
PlotRange ->
{{0, 1}, {0, 1}, {0, 1}},
PlotPoints -> 50,
MaxRecursion -> 7,
PlotRange -> All,
AxesLabel -> Automatic,
PlotLabel ->
StringForm["``", #[[1]]]] & /@
data,
SpanFromLeft, 4],
2] // Grid

f1<=1
always true, maybe you wan to setf1 < 1/8
for example. $\endgroup$