Cartesian Product of Subsets/Corollary 1
Jump to navigation
Jump to search
Corollary to Cartesian Product of Subsets
Let $A, B, S$ be sets such that $A \subseteq B$.
Then:
- $A \times S \subseteq B \times S$
Proof
From Set is Subset of Itself we have $S \subseteq S$.
From Cartesian Product of Subsets:
- $A \subseteq B \land S \subseteq S \implies A \times S \subseteq B \times S$
$\blacksquare$
Sources
- 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.9$: Cartesian Product: Exercise $1$