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nLeftarrow

Represents a negated double left arrow symbol, commonly used in mathematical logic and set theory to indicate non-implication.

Overview

Serves as a critical notation in formal mathematics and theoretical computer science for expressing negative logical relationships and contradictions.

  • Essential in proof writing to show that one statement does not imply another
  • Used in set theory to denote non-containment or non-subset relationships
  • Appears frequently in abstract algebra and topology when discussing counterexamples
  • Particularly useful in mathematical logic for expressing the negation of reverse implications

Examples

Showing that two mathematical statements are not logically equivalent.

P⇍QP \nLeftarrow Q 
P \nLeftarrow Q

Demonstrating non-implication in set theory.

A⊂B⇍B⊂CA \subset B \nLeftarrow B \subset C 
A \subset B \nLeftarrow B \subset C

Expressing that one condition does not follow from another in a mathematical proof.

x>0⇍x2>0x > 0 \nLeftarrow x^2 > 0 
x > 0 \nLeftarrow x^2 > 0