How to identify in a matrix if an X is listed in two columns of data

I have a table like the below:

Grocery Item	Store 1	Store 2	Store 3	Store 4	Vendor 1	Vendor 2	Vendor 3	Vendor 4
Apple	X	X			X	X
Orange		X	X		X		X
Pear			X				X	X
Banana				X		X	X	X

And want to create a formula that will tell me if a Vendor has any fruits in each store. This would populate the table below with an X if true (do not need to know which fruit, just if it provides any fruit to that store).

	Store 1	Store 2	Store 3	Store 4
Vendor 1
Vendor 2
Vendor 3
Vendor 4

For example, Vendor 1 in Stores 1, 2, and 3 = Yes, but Vendor 1 in Store 4 = No. Thanks for any help! I've attached an XLS of the above as well if that helps.

Sorry, I tried to make the table simpler to understand for this purpose. In my real spreadsheet, the Grocery Item is a communication topic, the Stores are communication vehicle (email, poster), and the Vendor is the audience (managers, executives, employees). I am trying to show which communication vehicles will go to which audiences. I've updated the example file to be more accurate if that helps.

Still don't understand the table!

Perhaps manually fill in the table and then it may be more apparent.

Added a new table with the matrix filled in.

Dave, this is exactly what I was looking for! Thank you! I knew it had to be related to Match and Index, but am not comfortable with those functions yet. I'm good to go now though, and have some good reading to learn-up for the future. :-)