The negation of '$$\forall x \in N, x^2+x$$ is even number' is

If $$\mathrm{p}$$ : It is raining.

$$\mathrm{q}$$ : Weather is pleasant

then simplified form of the statement "It is not true, if it is raining then weather is not pleasant" is

The negation of $$p \wedge(q \rightarrow r)$$ is

If $$\mathrm{p}$$ : It is raining and $$\mathrm{q}$$ : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is