Definition

Noun: The state or condition where two or more things cannot both exist, be true, or occur simultaneously. It describes a fundamental logical relationship of incompatibility.

Usage

This term is used to describe a logical, conceptual, or practical contradiction where the presence or truth of one element necessarily excludes the other(s). It is a formal term common in logic, philosophy, statistics, and technical discussions.

Examples

• In logic, the propositions "The door is open" and "The door is closed" exhibit mutual exclusiveness; they cannot both be true for the same door at the same time.
• The mutual exclusiveness of the two hypotheses meant that proving one automatically disproved the other.
• When designing the survey, we ensured the answer choices had mutual exclusiveness so a respondent could not select two contradictory options.

Advanced Usage

• In Probability Theory: Two events are said to be mutually exclusive if they cannot occur at the same time. The probability of both occurring together is zero.
  • Example: In a single coin toss, the outcomes "heads" and "tails" have mutual exclusiveness.
• In Set Theory: Two sets are mutually exclusive if their intersection is the empty set (they share no common elements).

Variants and Related Words

• Mutually Exclusive (adjective phrase): Describing things that possess mutual exclusiveness.
  • Example: "Being a square" and "being a circle" are mutually exclusive properties for a shape.
• Incompatibility (noun): A broader term for the inability to exist or work together harmoniously.
• Contradiction (noun): A specific type of incompatibility between statements or ideas.

Synonyms

• Incompatibility
• Disjointedness
• Contradictoriness
• Oppositeness (in specific contexts)

Antonyms

• Compatibility
• Concurrence
• Overlap
• Intersection

Noun

1. the relation between propositions that cannot both be true at the same time