$p \implies q$ or $q \implies p$ I am having a hard time translating English to logic with implications. It seems like $p \implies q$ is the same as $q \implies p$ a lot of the time.
For example: 

“You can access the Internet from campus only if you are a computer science major or you are not a freshman.”
  We let $a, c,$ and $f$ represent “You can access the Internet from campus,”
  “You are a computer science major,” and “You are a freshman,” respectively. Noting that “only
  if” is one way a conditional statement can be expressed, this sentence can be represented as
$a \implies (c \vee \neg f )$.

Why can't we say $(c \vee \neg f ) \implies a$?
This is confusing to me because the next example is

“You cannot ride the roller coaster if you are under $4$ feet tall unless you are older than $16$ years old.”
  Let $q, r,$ and $s$ represent “You can ride the roller coaster,” “You are under $4$ feet tall,” and “You are older than $16$ years old,” respectively. Then the sentence can be translated to
$(r \wedge \neg s) \implies ¬q$

These English sentences both seem to say "you can/cannot access $x$" if "you meet $y$ requirements"
yet the $a$ predicate is on the left hand side for the first example, and the $\neg q$ is on the right hand side for the second. I have looked around for answers but nothing has seemed to clear this up for me. It seems like you could switch both of these around.
Thanks for the help.
Edit:
I think my question may have got lost in my post, or maybe I'm not understanding the answers. My question is how do you know which sides of the implication do you put your propositional variables on? How do I know it is $p \implies q$ and not $q \implies p$?
 A: If "you can access the internet from the campus only if you are a computer science major of a freshman" is a true sentence then also the following sentence is true: "you can access the internet from the campus only if you are a computer science major". 
You are dealing with necessary conditions. They do not have to be sufficient. 
However, in daily language mostly all necessary conditions are mentioned (or are supposed to be mentioned). 
That makes the "bundle of conditions" sufficient after all.
The fact that we tend to expect that is the source of confusion.
A: *

*Your actual confusion is not over the direction of implication, but
due to “unless” and “only if” being particularly tricky to translate,
which is in turn because the colloquial meaning of each tends to be
loose.

For the next two points, note that $$A → B$$ is logically equivalent to $$(\text{not }A) \;∨\; B.$$


*Strictly speaking,
“$P$ unless $Q$”, “$P$ if not $Q$” and “$P$ or $Q$” all have the
same literal meaning, because satisfying the condition $Q$ does not
guarantee that $P$ results.


*In the absence of an appropriately-placed comma that would have
disambiguated the statement, we instead rely on real-world context,
and interpret

*

*You cannot ride the roller coaster if you are under $4$ feet tall unless you are older than $16$ years old
not as

*

*You cannot ride the roller coaster if (you are under $4$ feet tall,    unless you are older than $16$ years old),

but instead as

*

*(You cannot ride the roller coaster if you are under $4$ feet tall)    unless you are older than $16$ years old

*(You cannot ride the roller coaster if you are under $4$ feet tall)    if you are not older than $16$ years old

*If you are not older than $16$ years old, then (if you are under $4$ feet tall, then you cannot ride the roller coaster),

that is, $$\text{Age}\leq16 \;→\; \big(\text{Height}<4 \;→\; \text{Can't Ride}\big)\\
\text{Age}>16 \;∨\; \big(\text{Height}\geq4 \;∨\; \text{Can't Ride}\big)\\
\text{Can't Ride} \;∨\; \big(\text{Age}>16 \;∨\; \text{Height}\geq4\big)\\
\text{Can Ride} \;→\; \big(\text{Age}>16 \;∨\; \text{Height}\geq4\big),$$ or simply
$$\text{Age}>16 \:\:∨\:\: \text{Height}\geq4 \:\:∨\:\: \text{Can't Ride}.$$

Let $q, r,$ and $s$ represent “You can ride the roller coaster,” “You are under $4$ feet tall,” and “You are older than $16$ years
old,” respectively. Then the sentence can be translated to $(r
\wedge \neg s) \implies ¬q$

Yes, this is the contrapositive of, and thus equivalent to, the
final implication above.


*While it is tempting to interpret “$P$ only if $Q$” as “$P$ if $Q;$
otherwise, not $P$” (i.e., “$P$ if and only if $Q$”), it
actually just
means “$P$ implies $Q$”, because satisfying the condition $Q$ does
not guarantee that $P$ results.


*We disambiguate

*

*You can access the Internet from campus only if you are a computer science major or you are not a freshman
as

*

*You can access the Internet from campus only if (you are a computer science major or you are not a freshman)

*If you can access the Internet from campus, then (you are a computer science major or you are not a freshman),

that is, $$\text{Can Internet} \;→\; \big(\text{Is CS Major} \;∨\; \text{Isn't Freshman}\big),$$ as required.
A: This is, as Element118 has said, due to the difference between "if" and "only if" which is annoying to wrap your head around at first, but makes sense once you get it. The point is that the sentences
if $P$ then $Q$
and
$P$ only if $Q$
are two ways of representing the same thing. They both can be expressed as 
$P\implies Q$
so it's really just a subtlety of the language used. If I misunderstood and that's not where your problem lies, just let me know and I'll update this answer
