Convert the following to clausal form

Question

Convert below into the clausal form:

$$\forall\, x\,(\exists\,y\,(q(x)\wedge r(y))\to p(x))$$

I cannot solve this.

Answer 1

$a \implies b$ is equivalent to $\neg a \vee b$.

So you can express your sentence as:

$$ \forall x \: \neg(\exists y \: q(x) \wedge r(y)) \vee p(x)$$

Which is equivalent to:

$$ \forall x \: (\forall y \: \neg q(x) \vee \neg r(y)) \vee p(x)$$

And you can get rid of parentheses:

$$ \forall x \: \forall y \: p(x) \vee \neg q(x) \vee \neg r(y)$$