Question 1: Find the identity element in the set of all positive integers defined by for all,

Answer:

Given that binary operation is valid for set of all positive integers defined by

Let us assume and the identity element that we need to compute be

We know that the Identity property is defined as follows:

Therefore the required Identity element w.r.t is 0

Question 2: Find the identity element in the set of all rational numbers except with respect to defined by

Answer:

Given that binary operation is valid for a set of all rational numbers defined by

Let us assume and the identity element that we need to compute is

We know that the Identity property is defined as follows:

Therefore the required Identity element w.r.t is 0.

Question 3: If the binary operation on the set is defined by then element with respect to **[CBSE 2012]**

Answer:

Given that binary operation is valid for the set defined by

Let us assume and the identity element that we need to compute is

We know that he Identity property is defined as follows:

Therefore the required Identity element w.r.t is 5.

Question 4: On the set of integers, if the binary operation is defined by then find the identity element. **[CBSE 2012]**

Answer:

Given that binary operation is valid for the set of integers defined by

Let us assume and the identity element that we need to compute be

We know that he Identity property is defined as follows:

Therefore the required Identity element w.r.t