Question

Express the negations of each of these statements so that

all negation symbols immediately precede predicates.

∃x∃y(Q(x, y) ↔ Q(y, x))

Answer 1

$By \space steps: \space \\ 1)\forall \space x\forall \space y\neg(Q(x,y)\leftrightarrow \space Q(y,x))\\ 2)\forall \space x\forall \space y(Q(x,y) \space \oplus \space Q(y,x)) \\ where \space \oplus \space is \space exclusive \space and \space exhaustive\\ hence \space answer \space is \space ∀x∀y(Q(x,y)⊕Q(y,x))$