Write true or false for the following statement.
“The product of a positive and negative integer is negative”.

Hint:In order to state whether the given statement is true or false, we will try to apply the statement for two or three cases considering different integers and then we will deduce our answer from the observed values.

Complete step-by-step answer:
In this question, we have been asked whether the statement, “the product of a positive and negative integer is negative” is true or false. So, in order to solve this question, we will consider a few cases of one positive and one negative integer products.
So, let us consider $2\times \left( -3 \right)$. Now, we know that the product of a negative sign with a positive sign is negative. So, we can say that $2\times \left( -3 \right)=-\left( 2\times 3 \right)=-6$.
Now, let us consider $\left( -4 \right)\times 5$. The same rule will be applied here also, that is the product of a negative sign with a positive sign is negative. So, we can say that $\left( -4 \right)\times 5=-\left( 4\times 5 \right)=-20$.
In both the cases we have received the product as a negative integer. Therefore, we can say that the given statement, that is, “the product of a positive and negative integer is negative” is true.

Note: In the case of addition of a positive and a negative integer, after subtracting the smaller integer from the greater integer, the sign of the result will be taken as the sign of the integer with the greatest value. While, when we find the product of a positive and a negative integer, we don’t have to consider the sign of the result as the sign of the integer with the greatest value, because for multiplication of a positive and a negative integer, the result will always be a negative integer. So, this must be noted as this can be a mistake one might make.