The only problem I could see is that there should be two more cases: $x \in A$ and $y \in D$; and $x \in C$ and $y \in B$. Please suggest.
2026-03-29 13:27:16.1774790836
Finding a flaw in a proof that $(A\cup C)\times (B \cup D)\subseteq(A\times B)\cup(C\times D)$
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Yes, what you said is the error. The correct statement would be $$(A\cup C)\times(B\cup D)\subset(A\times B)\cup (A\times D)\cup (C\times B)\cup (C\times D)$$