If A × B
Question:

If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.

Solution:

Let:

$(x, y) \in(A \times B)$

$\therefore x \in A, y \in B$

Now,

$\because(A \times B) \subseteq(C \times D)$

$\therefore(x, y) \in(C \times D)$

Or

$x \in C$ and $y \in D$

Thus, we have :

$A \subseteq C \& B \subseteq D$

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