In logic, converse nonimplication is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication).

Converse nonimplication is notated ${\displaystyle P\nleftarrow Q}$, or ${\displaystyle P\not \subset Q}$, and is logically equivalent to ${\displaystyle \neg (P\leftarrow Q)}$ and ${\displaystyle \neg P\wedge Q}$.

The truth table of ${\displaystyle A\nleftarrow B}$.

Converse nonimplication is notated ${\textstyle p\nleftarrow q}$, which is the left arrow from converse implication (${\textstyle \leftarrow }$), negated with a stroke (/).

Alternatives include

falsehood-preserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of converse nonimplication

Example,

If it rains (P) then I get wet (Q), just because I am wet (Q) does not mean it is raining, in reality I went to a pool party with the co-ed staff, in my clothes (~P) and that is why I am facilitating this lecture in this state (Q).