Question 1195845
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Let
<font color=red>P = the moon is out</font>
<font color=blue>Q = we will start a campfire</font>
<font color=green>R = we will roast marshmallows</font>


The original conditional of "If <font color=red>the moon is out</font>, then <font color=blue>we will start a campfire</font> and <font color=green>we will roast marshmallows</font>" can be condensed to "If <font color=red>P</font>, then <font color=blue>Q</font> and <font color=green>R</font>" where P,Q,R were defined earlier above.


From that we can then write  <font color=red>P</font> --> ( <font color=blue>Q</font> and <font color=green>R</font>)
The arrow notation indicates an "if, then" conditional statement. 
Use parenthesis to have P lead to both Q and R simultaneously. 
It would be erroneous to write P --> Q and R because that might be misinterpreted as (P --> Q) and R


Lastly, replace the word "and" with the ampersand symbol to get <font color=red>P</font> --> ( <font color=blue>Q</font> & <font color=green>R</font>)


Side note: Some textbooks will use a center dot in place of an ampersand, or a wedge symbol denoted as ^


We have this symbolic form:
P --> (Q & R)


In your notes somewhere, you should have something that looks like this
<img width = "30%" src = "https://image1.slideserve.com/1838923/converse-inverse-and-contrapositive-n.jpg">
Image Credit: 
<a href = "https://www.slideserve.com/jaclyn/converse-inverse-and-contrapositive">https://www.slideserve.com/jaclyn/converse-inverse-and-contrapositive</a>


The original conditional p -> q leads to the inverse ~p -> ~q
The squiggly tilde marks mean "not", i.e. the opposite
Example:
p = it does rain
~p = it does not rain


Therefore, we'll have this inverse for this particular problem
~P --> ~(Q & R)


As your teacher mentioned, use <a href = "https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/17%3A_Logic/17.7%3A_De_Morgans_Laws">De Morgan's Law</a> to turn ~(Q & R) into ~Q v ~R
The v symbol is the opposite of the ampersand, it means "or"


p & q = p and q
p v q = p or q


So 
~P --> ~(Q & R)
is the same as
~P --> (~Q v ~R)
after applying De Morgan's Law


The last step is to translate back to English
P = the moon is out
~P = the moon is not out
Q = we will start a campfire
~Q = we will not start a campfire
R = we will roast marshmallows
~R = we will not roast marshmallows



~P --> (~Q v ~R)
translates to
If the moon is not out, then we will not start a campfire or we will not roast marshmallows. 


You can think of it like this
If (the moon is not out) ---> then (we will not start a campfire OR we will not roast marshmallows)


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<font color=red>Final Answer: Choice B</font>
If the moon is not out, then we will not start a campfire or we will not roast marshmallows. 
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