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NSPredicate that is the equivalent of SQL's LIKE

NSString *_mySearchKey = @"James";
NSPredicate *_myPredicate = [NSPredicate predicateWithFormat:@"(firstname CONTAINS[cd] %@) OR (lastname CONTAINS[cd] %@)", _mySearchKey, _mySearchKey];

The CONTAINS operator will certainly work just fine. If you're looking for a more direct correlation, then you can also use the LIKE operator (* = 0 or more characters, ? = 1 character):

NSString *_mySearchKey = @"James";
NSPredicate *_myPredicate = [NSPredicate predicateWithFormat:@"firstname LIKE '*%1$@*' OR lastname LIKE '*%1$@*'", _mySearchKey];

For reference:
https://developer.apple.com/library/content/documentation/Cocoa/Conceptual/Predicates/Articles/pSyntax.html#//apple_ref/doc/uid/TP40001795-215868


Another possibility

@"firstname beginswith[c] James"

As a nice alternative to contains

Sometimes contains isn't always the right answer