Question

Is it correct to say A×A={(a,a):a belongs to A}?

Answer 1

No, I think it should be A x A = {(a, b) : a,b ∈ A}.

Answer 2

Answer:

No.

Step-by-step explanation:

No, it is not correct. The correct version is , A×A = {(a, b) : a, b ∈ A } . When you write A×A = {(a, a) : a ∈ A}, it signifies that AxA consists of ordered pairs of same arguments only which is wrong. By definition, it should have contained all possible ordered pair (a, b) where a, b ∈A not only (a, a). For example, if A ={1, 2, 3 } then, A×A = {(1, 1),(1, 2),(1, 3),(2, 1),(2,2), (2, 3), (3, 1), (3, 2), (3, 3)} and

not {(1, 1), (2, 2), (3, 3)} .