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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The 14th and 15th amendments of the Constitution of the United States
Amendments are proposed by a two-thirds vote from Congress. An amendment can also be proposed by a convention called by Congress, if two-thirds of the states request it.
article 5 says that congress may propose amendments by 2/3 vote in each house, or by a national convention of delegates from each state.
Amendments are considered apart of the theconstitution with the same enforcement value. I believe the constitution says amendments have the same "intents and purposes" as the rest of the constitution.Amendments can be passed in two ways: 1) Congress can propose an amendment to the states by a 2/3 majority vote in each house. Then if 3/4 of the states ratify it..it becomes an amendment.2) 2/3 of the states call a convention to propose amendments. If 3/4 of all the states ratify those proposals; they become amendments.
There are four amendments that deal with voting rights. They are the 15th, 19th, 24th, and 26th Amendment.