#### Question

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

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

#### Solution

Define an operation * on **N** as:

*a *** b* = *a + b* ∀ *a, b *∈ **N**

Then, in particular, for *b* = *a* = 3, we have:

3 * 3 = 3 + 3 = 6 ≠ 3

Therefore, statement (i) is false.

Is there an error in this question or solution?

Solution State Whether the Following Statements Are True Or False. Justify. for an Arbitrary Binary Operation * on a Set N, A * A = ∀ A A * N. Concept: Concept of Binary Operations.