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**Hint:**In this question, first of all fetch for an example where the statement would go wrong. Then by taking an example for each statement prove that the statement is wrong or right. So, use this concept to reach the solution of the given problem.

__Complete step-by-step answer__:Given statements are

p: when a positive integer and a negative integer are added we always get a negative

q: when two negative integers are added, we get a positive integer

To know whether the statement p is true or false, let us consider an example.

For example: let the positive integer be 7 and the negative integer be \[ - 4\]. By adding up them we have \[7 + \left( { - 4} \right) = 7 - 4 = 3\] which is a positive integer.

But given that the result would be a negative integer.

Hence the statement p is false.

To know whether the statement q is true or false, let us consider an example.

For example: let the two negative integers be \[ - 6, - 2\]. By adding up them we have

\[ - 6 + \left( { - 2} \right) = - 6 - 2 = - 8\] which is a negative integer.

But given that the result would be a positive integer.

Hence the statement q is also false.

**Thus, the correct option is D. Both p and q are false.**

**Note**: A integer is defined as a number that can be written without a fractional component. Positive integers are integers that are greater than zero and negative integers are integers that are less than zero. In this question if we can`t find an example to prove the statement is wrong then that statement is true.

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