It seems that cancel and cancel out can be used in the same way. For example, A cancels B or A cancels out B. In which context is one preferred over the other?
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Cancel out is a Phrasal Verb, extending the sense of the verb cancel with the completive aspectual sense of out.
Some other examples:
The out produces the complete cancellation sense, but that's also available with cancel alone since it can mean 'to delete'. This is especially true with a Reciprocal construction like each other.
All of the following, for example, are grammatical, and equivalent in meaning.
As can be seen, Phrasal Verbs have interesting and complex syntax, especially the transitive ones.
When two things cancel each other out it means they "neutralize" each other, resulting in "zero." An example of this would be a sound cancelled out by another sound with inverted phase; by combining such two sounds, they cancel each other out and no sound is audible - the result is zero.
On the other hand, when something cancels something else, one of the two elements of cancellation still remains "active" even after the process. A user can cancel a computer process, for example. The user doesn't "disappear" after it happens.
If A cancels B = A remains existent, B becomes nonexistent.