Match two values in two columns and return yes if there appear in a different sheet

I am trying to figure out if a list of instrument serial numbers and their customer names that I have in Sheet 2 appear as part of a larger spreadsheet in Sheet 1.

In Sheet 1, serial numbers are in column A and names are in column M. In Sheet 2, serial numbers are in column B and names are in column C.

I can return B2 in D2 of Sheet 2 using the formula:

=VLOOKUP(B2, 'Sheet 1'!A:A, 1, FALSE)

However, that does not match columns B and C, so I've been playing with the following formula for column D of sheet 2 (doesn't work, but it's what I think is the start to something):

=MATCH(1,IF(B2='Sheet 1'!$A:A, IF(C2='Sheet 1'!M:M,1,0),0),0)

My questions:

1. How do I correctly confirm that B2 and C2 appear in the same row of Sheet 1?

2. Is there a better function than VLOOKUP that outputs "TRUE", "1", or the statement of my choosing ("yes") if a match is found?