State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.

If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$

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True

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State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.

If $A$ and $B$ are non-empty sets, then $A \times B$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in A$ and $y \in B.$

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