Q12 of 107 Page 24

State whether the following statements are true or false. Justify.

For an arbitrary binary operation ∗ on a set N, a ∗ a = a ∀a ∈ N.

For an arbitrary binary operation ∗ on a set N, a ∗ a = a ∀a ∈ N.

The above statement is false.


Explanation: It is given that an operation ∗ on a set N, a ∗ a = a ∀a ∈ N


Then, in particular, for b = a = 3, we get,


3 * 3 = 3 + 3 = 6 ≠ 3


More from this chapter

All 107 →
10

Find which of the operations given above has identity.

 11

Let A = N × N and ∗ be the binary operation on A defined by

(a, b) ∗ (c, d) = (a + c, b + d)


Show that ∗ is commutative and associative. Find the identity element for ∗ on


A, if any.

 12

State whether the following statements are true or false. Justify.

If ∗ is a commutative binary operation on N, then a ∗ (b ∗ c) = (c ∗ b) ∗ a

 13

Consider a binary operation ∗ on N defined as a ∗ b = a3 + b3. Choose the correct answer.