Calculating derived values

Question

I am trying to work out how to write an intuitive formula in google-sheets that, given two tables (of booleans) with dimensions AxB, CxB, one generates the correlating table CxA following boolean OR.

What formula can be used to generate the table CxA? I definitely want the table to be filled using a single cell formula.

I have been thinking of using map, byrow, bycol or scan, but each time I start out I get lost in the matrix.

The tables below highlight the case where R is true for [a,e]; [1,2,3,6] are true for a; and [3,4,6] are true for e:- therefore [1,2,3,4,6] are true for R.

AxB	R	B	G	K
a	1	0	0	0
b	0	0	0	1
c	0	1	1	0
d	0	1	0	0
e	1	1	0	0

CxB	1	2	3	4	5	6
a	1	1	1	0	0	1
b	0	0	1	0	1	0
c	0	1	0	1	1	0
d	1	1	0	1	1	0
e	0	0	1	1	0	1

CxA	1	2	3	4	5	6
R	1	1	1	1	0	1
B	1	1	1	1	1	1
G	0	1	0	1	1	0
K	0	0	1	0	1	0

Answer 1

You may try:

=index(sign(mmult(transpose(C3:F7),K3:P7)))