Answer to Question #262184 in Discrete Mathematics for Abhi

Question

  Let P (x, y) be a predicate. What is the negation of ∃x ∀y(P (x, y) ⇐⇒ P (y, x))?

Answer 1

$\forall x \exists y(\neg (P (x, y)\implies P (y, x)\land P (y,x)\implies P (x,y)))$

$\forall x$ is negation of $\exist x$

$\exists y$ is negation of $\forall y$

$\neg (P (x, y)\implies P (y, x)\land P (y,x)\implies P (x,y))$ is negation of $(P (x, y) ⇐⇒ P (y, x))$