Question

DISCRETE STRUCTURE COMPUTING

5. Prove whether it is possible to have a cartesian product A x A containing only (a,b) when a + b.

Answer 1

Answer:------------

If A and B are two non-empty sets, then their Cartesian product A × B is the set of all ordered pair of elements from A and B.

A × B = {(x, y) : x ∈ A, y ∈ B}

According to question,
(i)
Suppose we have , A = { 1,2 }
So,
A x A = { 1,2 } x { 1,2 } = { (1,1), (1,2), (2,1), (2,2) }

(ii)
Suppose we have , A = { ∅,1 }
So,
A x A = { ∅,1 } x{ ∅,1 } = { (∅,∅,), (∅, 1), (1, ∅,), (1,1) } = { ∅, 1, 1, 1 } = { ∅, 1 }
Hence , It is possible.