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