a$)$ Rewrite the following statement formally using quantifiers and variables.

Every emotion has an equal and opposite emotion.

$($c$)$ Write a negation for the statement in Part $($a$)($formally using quantifiers and variables$).$

$($b$)$ The following is the definition for limx$$a f$($x$)=$ L:

For every real number $>0,$ there exists a real number $>0$ such that for every real number x$,$ if

$|$x $$ a$|<$ and x $6=$ a then $|$f$($x$)$ L$|<.$

Write what it means for limx$$a f$($x$)6=$ L$.$ In other words, write the negation of the definition.