Describes two or more things that by definition cannot both be true at the same time.
"If it is X, then it cannot be Y, and if it is Y, then it cannot be X" means "X and Y are mutually exclusive."
For example if most participants said yes, then it is not true that all participants said yes. "Most," by definition, means "far more than not, but not all" and "all" means "without even one exception." Even though "most" and "all" both mean "a lot," they cannot both be true of the same thing at the same time.
If something is an even number, then it is by definition not an odd number.
If an animal is a cat, then it is by definition not a dog or mouse or snake.
"In Western culture, most religions are mutually exclusive. If you are a Muslim, you not a Jew. If you are an Baptist Christian, then you are not a Catholic Christian. It is hard for many Westerners to understand that there are people in Japan who practice both Shintoism and Buddhism at the same time and that this is thoroughly normal."
(Please retain the reference in reprint: http://www.letpub.com/index.php?page=author_education_mutually_exclusive)