Check to see if two inputs share the same data

I've attached a spreadsheet that has a data table in cells B3:E6. On the left side is a list of categories, from 1 to 3. The data to the right of this list (in cells C4:E6) is data based on these categories. For example, category 1 has the following data: 'circle', 'square' and 'triangle'. I would like to create something, as shown in examples A and B, where I can input these categories ranging from 1 to 3 in the green-filled areas, and an output is automatically generated in the orange-filled areas. This output will be based on what data is shared by the categories selected.

In example A, I have inputs '1' and '2'. If you look at the data table, the word 'triangle' is shared between 1 and 2 (cells E4 and E5). This is the only output.
In example B, I have inputs '1', '2', and '3'. If you look at the data table, the words 'circle' and 'square' are shared between '1' and '3' (C4:D4 and C6:D6). So, the output has both of these shapes for '1' and '3'. The only other output is 'triangle', as this is shared between '1' and '2'.

Could somebody please help me with a formula that can generate said outputs?

Thank you.

Cross link: https://www.mrexcel.com/board/thread...-data.1224575/

I am positive I could do this with VB, but the challenge is to do it with formulas. Perhaps the following will inspire someone smarter than me.

The Table is a truth table. So, if you look at column 1, it tells you that triangle is common to 1 and 2 and that both circle and square are common to 1 and 3. If you look at column 2, it tells you triangle is common with 1 but nothing is common with 3. If you look at column 3, circle and square are common with 1 and nothing is common with 2.

The truth is out there, but how do we create the table (there are formulas in the table) and how do we "collect" the intersections without VB?

I'm not sure about functions in 2013 so I use & for connecting strings in formula.

Helper 1 check duplicate of words.

G4
=COUNTIF($C$4:$E$6,C4)

Helper 2 list words that have multiples occur.

K4
=IF(G4>1," "&C4,"")

Output join them all

O4
=SUBSTITUTE(SUBSTITUTE(TRIM(K4&L4&M4)," ",","),",",", ")

Regards,