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## Main Question or Discussion Point

Can you prove the following theory of cardinality for a Cartesian product, -

[itex]\left|\:A\:\right|\:\leq\:\left|\:A\:\times\:B\:\right|\: if\: B\neq\phi[/itex]

In English,

The cardinality of a set [itex]A[/itex] is less than or equal to the cardinality of Cartesian product of A and a non empty set [itex]B[/itex].

[itex]\left|\:A\:\right|\:\leq\:\left|\:A\:\times\:B\:\right|\: if\: B\neq\phi[/itex]

In English,

The cardinality of a set [itex]A[/itex] is less than or equal to the cardinality of Cartesian product of A and a non empty set [itex]B[/itex].