Given,
A × B ⊆ C x D and A ∩ B ∈ ∅
To prove : A ⊆ C and B ⊆ D
A × B ⊆ C x D denotes A × B is subset of C × D that is every element A × B is in C × D
And A ∩ B ∈ ∅ denotes A and B does not have any common element between them.
A × B = {(a, b): a ∈ A and b ∈ B}
Since,
A × B ⊆ C x D (Given)
∴We can say (a, b) C × D
⇒ a ∈ C and b ∈ D
⇒ A ∈ C and B ∈ D
(A and B does not have common elements)
