Google sheets - Check all TRUE per row in boolean 2D array with ARRAYFORMULA

Question

I have the following data (created through a ARRAYFORMULA formula):

	A	B	C	D
1	TRUE	TRUE	FALSE	TRUE
2	TRUE	TRUE	TRUE	TRUE
3	TRUE	FALSE	TRUE	TRUE

If in a row all values are TRUE, the output for that row should be TRUE. If even 1 is FALSE, it should be FALSE instead. So a formula on the above table should output this:

	E
1	FALSE
2	TRUE
3	FALSE

Restrictions

• The 1st table's size is not fixed. There could be more columns or rows. Therefore, no manual row by row check.
• It should be 1 function that outputs to multiple rows (like the 2nd table), therefore it should be through the ARRAYFORMULA formula (not dragging a cell down, as this works badly when adding rows/columns at a later stage).

What I tried

AND

AND, but that gives only a single output:

=AND(A1:D3)
# FALSE

Also, AND doesn't work with ARRAYFORMULA

*

A * function as AND in ARRAYFORMULA:

=ARRAYFORMULA(A1:A3*B1:B3*C1:C3)

Problems are:

• This is a manual process, which doesn't scale.
• If a column is added later, it will become e.g. A1:A3*C1:C3*D1:D3 instead of A1:A3*B1:B3*C1:C3*D1:D3

A1:C3*

Unfortunately, this logic is not accepted:

=ARRAYFORMULA(A1:C3*)

QUERY

Maybe a QUERY can provide this logic? But I'm not able to come up with how that query should look like.

Question

How do I do a row-wise check if all values are TRUE with a single ARRAYFORMULA function (taking into account the restrictions mentioned)?

Answer 1

try:

=INDEX(REGEXMATCH(FLATTEN(QUERY(TRANSPOSE(B1:E3*1),,9^9)), "0")=FALSE)