QUIZ

\(p(a)∧q(y)\)

\(∀x(p(a)∧q(y))\)

\(∀x((p(x)∧q(y))[x:=a])\)

\(∀x(p(x)∧(q(y)[x:=a]))\)

\(∀x(p(x)∧q(y))\)

\(∀x(p(x)∨q(x,y))\)

\(∀x (p(x)∨q(x,f(x,y)))\)

\(∀x (p(x)∨q(x,f(w,y)))\)

\(∀w1 (p(w1)∨q(w1,f(w2,y)))\)

\(∀w (p(w)∨q(w,f(x,y)))\)

\(∃x∃z (p(x) ⇒ q(y,z))\)

\(∃w1 ∃w2 (p(f(w2,y)) ⇒ q(y,w2))\)

\(∃x∃z(p(f(z,y))⇒q(y,z))\)

\(∃z(p(f(z,y))⇒q(y,z))\)

\(∀x∃z p(x,f(w,y),z)\)

\(∀x∃wp(x,f(z,y),w)\)

\(∀x∃w1 p(x,f(w2,y),w1)\)

\(∀x∃z p(x,f(z,y),z)\)

\(∀x∃z p(x,y,z)\)