Question $1.$ Use the valid argument rules of inference to deduce the conclusion from the premises, giving a reason for each step.

a$.pq$

b$.rvvs$

c$.st$

d$.qvvs$

e$.s$

f$.p^{{?}^{?}}ru($Note: this means $(p^{{?}^{?}}r)u)$

g$.wvvt$

h$.$ :$.u^{{?}^{?}}w$

Question $2.$ Suppose the domain for both $x$ and $y$ is $N.$ Are these statements true or false? Explain.

AAx,EEy such that $)=(0.$

EEy such that $)=(0.$

AAx,EEy such that $)=(0.$

Question $3.$ Given a function $f(x)$ with domain $D,$ and numbers ainD and $L$ the formal meaning of $\underset{xa}{lim}f(x)=L$ can be expressed as

$AAlon>0,EE>0$ such that AAxinD,

Write the negation of this universal existential universal conditional statement $($in a positive way, i$.$e$.$ without a negation in front of any quantifiers$).$