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I assume that negative testing is an approach to design the test cases and so is equivalence partitioning. But I am not sure if NT is a part of ET.

An example:
A field can accept a numeric value from the range 0-10.

So I have three partitions: to 0, from 0-10 and more than 10. Another invalid partitions would represent letters which is also negative testing, isn't it?

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I would not classify equivalence partitioning as a negative test. Equivalence partitioning is about reducing the cost of testing, while achieving the same coverage. In your example above, equivalence partitioning allows you to test just 1 number in the 0-10 range, and use that test to stand for the whole range. Exhaustive testing, you would test the full range (11 tests), verses a single sample (1 test). It's more about being more efficient.

Boundary testing could be considered negative testing. In your example, testing behavior at -1, 0, 10, 11 is an example of boundary testing. Also, other input types (floating point, characters, etc.) are considered negative tests.

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