Given: A × B ⊆ C × D and A × B ≠ ϕ
Need to prove: A ⊆ C and B ⊆ D
Let us consider, (x, y) (A × B)......... (1)
⇒ (x, y)∈(C × D) [as A × B ⊆ C × D] .......... (2)
From (1) we can say that,
x∈ A and y∈B .......... (a)
From (2) we can say that,
x∈C and y∈D ....... (b)
Comparing (a) and (b) we can say that,
⇒ x∈A and x∈C
⇒ A ⊆ C Again,
⇒ y∈B and y∈D
⇒ B ⊆ D [Proved]
