 Hi and welcome to the session. Today we will learn about properties of addition and subtraction of integers. First of all, let us see closure under addition. This states that integers are closed under addition. In general, for any two integers a and b, a plus b is an integer. Let us take one example for this. Suppose we are given two integers minus 9 and 15, then minus 9 plus 15 is equal to 6, which is an integer. So, we can say that integers are closed under addition. Now, next property is closure under subtraction. This states that integers are closed under subtraction. In general, if a and b are two integers, then a minus b is also an integer. Let us take an example. Here we are given two integers 15 and minus 9. So, 15 minus minus 9 is equal to 24, which is an integer. Thus, integers are closed under subtraction. Now, let us learn about commutative property. This property states that addition is commutative for integers. In general, for any two integers a and b, a plus b is equal to b plus a. For example, let us take two integers minus 3 and 11. So, we have minus 3 plus 11 is equal to 11 plus minus 3, which is equal to subtraction is not commutative for integers. Next is associative property. This states that addition is associative for integers. In general, for integers a, b and c, a plus b plus c the whole is equal to a plus b the whole plus c. For example, suppose we are given three integers minus 5, 3 and minus 2, then minus 5 plus minus 2 the whole is equal to minus 5 plus 3 the whole plus which is equal to minus. Lastly, we have additive identity. So, let us see what is the additive identity for integers. Here, 0 is an additive identity for integers. That is, for any integer a, a plus 0 is equal to 0 plus a is equal to a itself. For example, for the integer minus 9 minus 9 plus 0 is equal to 0 plus minus 9 which is equal to minus 9 itself. Thus, we have that 0 is the additive identity for integers. Thus, in this session, we have learnt the properties of addition and subtraction of integers. And with this, we finish this session. Hope you must have understood all the properties. Goodbye, take care and have a nice day.