Definition

Adjective: Unable to be both true or to occur at the same time; if one is true or happens, the other must be false or cannot happen. This describes a relationship between two or more things, options, or statements where they completely oppose each other and cannot coexist.

Usage

The phrase "mutually exclusive" is used to describe conditions, events, categories, or choices that cannot occur together. It is often used in logic, statistics, probability, and everyday decision-making. - It typically follows a linking verb like "are" or "is." - It can be used before a noun as a compound adjective (e.g., "mutually exclusive options"). - It describes the relationship between two or more items.

Examples

• Logic/Argument:
  • The two theories about the crime are mutually exclusive; if one is correct, the other must be wrong.
• Choices/Options:
  • For this application, you must choose Plan A or Plan B; they are mutually exclusive and you cannot select both.
• Categories:
  • In this survey, the age groups 18-25 and 26-35 are mutually exclusive; a person can only belong to one.

Advanced Usage

• In Probability and Statistics: Two events are mutually exclusive if they cannot happen at the same time. The probability of both occurring together is zero.
  • In a single coin toss, the outcomes "heads" and "tails" are mutually exclusive.
• Formal Logic: Two propositions are mutually exclusive if the truth of one implies the falsity of the other.
  • The statements "The door is open" and "The door is closed" are mutually exclusive.

Variants and Related Words

• Mutual exclusivity (noun): The state or condition of being mutually exclusive.
  • The mutual exclusivity of the two hypotheses simplifies the testing process.
• Incompatible (adjective): Similar in meaning, but often implies things cannot work or exist together harmoniously, not just logically.
  • Their work schedules are incompatible. (This suggests a conflict, not necessarily a logical impossibility in the same way as "mutually exclusive.")

Synonyms

• Contradictory: Directly opposing, so that both cannot be true.
• Incompatible: Not able to exist or work together without conflict.
• Opposed: In conflict or contrast with.

Antonyms

• Compatible: Able to exist or occur together without conflict.
• Overlapping: Sharing some common area or characteristics; not exclusive.
• Simultaneous: Occurring or operating at the same time.

Adjective

1. unable to be both true at the same time