Proposition. All EECS $203$ students are from Michigan.

Incorrect Proof. Let m be the proposition that all EECS $203$ students are from Michigan,

and let A$($x$)$ be the predicate that student x is from Ann Arbor. Notice that we have

$$

$$x A$($x$)$

$->$ m$,$

that is$,$ if all EECS $203$ students are from Ann Arbor then they are all from Michigan. We

next rearrange this expression using our logical equivalence laws:

$$

$$

$$x A$($x$)$

$$ m implication breakout $$

$$x $$A$($x$)$

$$ m DeMorgan

$$x

$$

$$A$($x$)$ m

$$x

$$

A$($x$)->$ m

$.$ implication breakout

The last line states that, if there exists an EECS $203$ student from Ann Arbor, then m is

true. We have checked the roster and there does indeed exist an EECS $203$ student from

Ann Arbor, so we conclude that m is true.