document.write( "Question 1195845: Write the Inverse for the following statement. (Convert the statement into symbolic form, write the inverse, then use DeMorgan' s laws to transform it.) If the moon is out, then we will start a campfire and we will roast marshmallows.\" If we start a campfire and we roast marshmallows, then the moon is out. If the moon is not out, then we will not start a campfire or we will not roast marshmallows. If the moon is not out, then we will start a campfire but we will not roast marshmallows. If we do not start a campfire or we do not roast marshmallows, then the moon is not out. \n" ); document.write( "
Algebra.Com's Answer #828438 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Let
\n" ); document.write( "P = the moon is out
\n" ); document.write( "Q = we will start a campfire
\n" ); document.write( "R = we will roast marshmallows\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The original conditional of \"If the moon is out, then we will start a campfire and we will roast marshmallows\" can be condensed to \"If P, then Q and R\" where P,Q,R were defined earlier above.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From that we can then write P --> ( Q and R)
\n" ); document.write( "The arrow notation indicates an \"if, then\" conditional statement.
\n" ); document.write( "Use parenthesis to have P lead to both Q and R simultaneously.
\n" ); document.write( "It would be erroneous to write P --> Q and R because that might be misinterpreted as (P --> Q) and R\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Lastly, replace the word \"and\" with the ampersand symbol to get P --> ( Q & R)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Side note: Some textbooks will use a center dot in place of an ampersand, or a wedge symbol denoted as ^\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We have this symbolic form:
\n" ); document.write( "P --> (Q & R)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In your notes somewhere, you should have something that looks like this
\n" ); document.write( "
\n" ); document.write( "Image Credit:
\n" ); document.write( "https://www.slideserve.com/jaclyn/converse-inverse-and-contrapositive\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The original conditional p -> q leads to the inverse ~p -> ~q
\n" ); document.write( "The squiggly tilde marks mean \"not\", i.e. the opposite
\n" ); document.write( "Example:
\n" ); document.write( "p = it does rain
\n" ); document.write( "~p = it does not rain\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Therefore, we'll have this inverse for this particular problem
\n" ); document.write( "~P --> ~(Q & R)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As your teacher mentioned, use De Morgan's Law to turn ~(Q & R) into ~Q v ~R
\n" ); document.write( "The v symbol is the opposite of the ampersand, it means \"or\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "p & q = p and q
\n" ); document.write( "p v q = p or q\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So
\n" ); document.write( "~P --> ~(Q & R)
\n" ); document.write( "is the same as
\n" ); document.write( "~P --> (~Q v ~R)
\n" ); document.write( "after applying De Morgan's Law\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The last step is to translate back to English
\n" ); document.write( "P = the moon is out
\n" ); document.write( "~P = the moon is not out
\n" ); document.write( "Q = we will start a campfire
\n" ); document.write( "~Q = we will not start a campfire
\n" ); document.write( "R = we will roast marshmallows
\n" ); document.write( "~R = we will not roast marshmallows\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "~P --> (~Q v ~R)
\n" ); document.write( "translates to
\n" ); document.write( "If the moon is not out, then we will not start a campfire or we will not roast marshmallows. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can think of it like this
\n" ); document.write( "If (the moon is not out) ---> then (we will not start a campfire OR we will not roast marshmallows)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Final Answer: Choice B
\n" ); document.write( "If the moon is not out, then we will not start a campfire or we will not roast marshmallows.
\n" ); document.write( " \n" ); document.write( "
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