Prove that the number of exhaustive test cases to be writen in a test case plan for n number of inputs is 2^n?

Question

Please give complete answer with details.

Answer 1

Example test condition: If a numeric value between 1 and 5 is entered, its double is displayed else an error message is displayed.

The following test cases will be required to test this:

1) Entering any value between 1 and 5 should display the value's double.

2) Entering any numeric value not between 1 and 5 or any alphanumeric value or any value with special characters should display the error message.

As this example shows, one input can be tested by two (2^1) test cases - one positive test case and one negative test case. Likewise, two input test conditions will need four (2^2) test cases - two positive test cases and two negative test cases. And so on.

Inder P Singh