State whether the following statements are true or false. Justify. For an arbitrary binary operation ∗ on a set N, a ∗ a = a ∀ a ∈ N.

Question

Philoid · Accepted Answer

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