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They don't cancel each other but the 1st and 14th sometimes conflict- for example the government may step into a Church matter if it's an equal protection issue like gay rights, although they are not supposed to. Perhaps others can provide more examples.

Additional thought:

There are no amendments that cancel each other out. The Twenty-First Amendment supersedes the Eighteenth Amendment. Congress passed the Volstead Act in 1919, allowing them to enforce the Eighteenth Amendment (Prohibition), and the Twenty-first Amendment ended Prohibition. The earlier amendment doesn't cancel the later amendment.

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Q: Which two amendments cancel each other?
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