NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Express each of these statements using predicates, quantifiers, logical connectives, and mathematical operators where the domain consists of all integers.

The average of two positive integers is positive.

Multiple Choice

$$

x $$

y$(($x $>0)$

$($y $>0)$

$(($x $+$ y$)/2>0))$

$$

x $$

y$(($x $<0)$

$($y $<0)->(($x $+$ y$)/2>0))$

$$

x $$

y$(($x $>0)$

$($y $>0)$

$(($x $+$ y$)/2>0))$

$$

x $$

y$(($x $<0)$

$($y $<0)->(($x $+$ y$)/2>0))$

$$

x $$

y$(($x $>0)$

$($y $>0)->(($x $+$ y$)/2>0))$