Consider two contradictory statements—“All lemons are yellow” and “Not all lemons are yellow”—and suppose that both are true. If that is the case, anything can be proven, e.g., the assertion that “unicorns exist”, by using the following argument:
We know that "Not all lemons are yellow", as it has been assumed to be true.
We know that "All lemons are yellow", as it has been assumed to be true.
Therefore, the two-part statement "All lemons are yellow or unicorns exist" must also be true, since the first part "All lemons are yellow" of the two-part statement is true (as this has been assumed).
However, since we know that "Not all lemons are yellow" (as this has been assumed), the first part is false, and hence the second part must be true to ensure the two-part statement to be true, i.e., unicorns exist.
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