document.write( "Question 804234: Given the implication \" you brush your hair, then your hair will be shiny\" answer the following questions
\n" ); document.write( "1. what is the converse of the given implication?
\n" ); document.write( "2. what is the inverse of the given implication?
\n" ); document.write( "3. what is the contra positive of the given implication?\r
\n" ); document.write( "\n" ); document.write( "4. If given the converse statement \" If you are broke , then you spent a lot of money\" what was the original implication?
\n" ); document.write( "5. If given the contra positive statement, \" If school is not cancelled then we did not have a blizzard\", what was the original implication.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #489012 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Original implication = p → q    (if p, then q) \r\n" );
document.write( "Inverse = ~p → ~q               if not p, then  not q)\r\n" );
document.write( "Converse = q → p                if q, then p\r\n" );
document.write( "Contrapositive = ~q → ~p        if not q, then not p\r\n" );
document.write( "

\n" ); document.write( "Given the implication \"If you brush your hair, then your hair will be shiny\"
\n" ); document.write( "
\r\n" );
document.write( "Let p = \"You brush your hair\".\r\n" );
document.write( "Let q = \"Your hair is shiny\".\r\n" );
document.write( "\r\n" );
document.write( "Notice the change in the tense of the verb in q from \"will be\" to \"is\".\r\n" );
document.write( "This is allowed to keep the statements from sounding funny, and as they might\r\n" );
document.write( "be spoken in reality.\r\n" );
document.write( "\r\n" );
document.write( "p → q = \"If you brush your hair, then your hair will be shiny\"\r\n" );
document.write( "

\n" ); document.write( " answer the following questions
\n" ); document.write( "1. what is the converse of the given implication?
\n" ); document.write( "
\r\n" );
document.write( "q → p = \"If your hair is shiny, then you have brushed your hair\"\r\n" );
document.write( "

\n" ); document.write( "2. what is the inverse of the given implication?
\n" ); document.write( "
\r\n" );
document.write( "~p → ~q = \"If you do not brush your hair, then your hair will not be shiny\"\r\n" );
document.write( "

\n" ); document.write( "3. what is the contrapositive of the given implication?
\n" ); document.write( "
\r\n" );
document.write( "~q → ~p = \"If your hair is not shiny, then you have not brushed your hair\"\r\n" );
document.write( "
---------------------------------------------------------
\n" ); document.write( "4. If given the converse statement \" If you are broke , then you spent a lot of money\" what was the original implication?
\n" ); document.write( "
\r\n" );
document.write( "Given converse = q → p = \"If you are broke , then you spent a lot of money\"\r\n" );
document.write( "\r\n" );
document.write( "q = \"You are broke\"\r\n" );
document.write( "p = \"You spent a lot of money\" \r\n" );
document.write( "\r\n" );
document.write( "Original implication = p → q = \"If you spent a lot of money, then you are broke.\"\r\n" );
document.write( "
----------------------------------------------------------------
\n" ); document.write( "5. If given the contra positive statement, \" If school is not cancelled then we did not have a blizzard\", what was the original implication.
\n" ); document.write( "
\r\n" );
document.write( "Given contrapositive = ~q → ~p = \"If school is not cancelled then we did not have a blizzard\r\n" );
document.write( "\r\n" );
document.write( "q = School is canceled\r\n" );
document.write( "p = We had a blizzard\r\n" );
document.write( "\r\n" );
document.write( "Original implication = p → q = If we had a blizzard, then school was canceled.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );