Question $3$: $($Hint: what inference rules apply?$)1.$ What would be the result of applying the If$-$Then inference rule on the following hoare triples: $($p $$ q$)($p $$ r$)($q $$ r$)($p $$ q$)($p $$ r$)\{$q $$q$\}($q $$ r$)12.$ What can we conclude given the following two lines are true: p $$q $\{$r $$ q$\}($p $$ r$)$ p $$q $\{$r $$q$\}($p $$ r$)3.$ What is the post$-$condition that makes the following Hoare triple valid? x $=($i $+1)!2$i $3$ i$1\{$i $$ i $+1\}(???)4.$ Suppose we are given the following Hoare triple: $($x $10)($y $>10)\{$x $$x$\}($x $<$ y$)$ What else would we need to know in order to apply the if$-$then inference rule to conclude the following line? $($y $>10)\{$if$($x $10)$ then x $$x$\}($x $<$ y$)5.$ If we are given the following two Hoare triples, what can we conclude? $($x $$ i$)($x $=$ i $2)\{$x $$ x $+$ x$\}($x $=2$i $2)($x $<$ i$)($x $=$ i $2)\{$x $$ x $+$ i$2\}($x $=2$i $2)$