MATL, 5 bytes
:i\~z Input isInputs are a cell array containing the start and end values, and then a column vector defining list.
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Explanation
: % Range, with implicit input: cell array {start, end}. This gives the range % from start to end i % Input: list of numbers in the form of a column vector \ % Modulo, with boradcast. This gives a matrix with each number in the range % modulo each number in the list ~ % Logical negation z % Number of nonzero entries. Implicit display