document.write( "Question 79708: 29: The converse of the statement: \"If you are baking brownies, then the kitchen smells good\", is \"If the kitchen smells good, then you are baking brownies.\" \n" ); document.write( "

Algebra.Com's Answer #57209 by doctor_who(15) $\"\"$ $\"About$

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No, not necessarily. The kitchen might smell good because you are roasting some coffee.\r
\n" ); document.write( "\n" ); document.write( "What's the application to maths ? Well, it is in the area of logic. Without getting too detailed, the first statement \"if you are baking brownies .. then..\" is a statement of the form \"If A then B\" and we are investigating if the converse is always true, ie IF B THEN A.\r
\n" ); document.write( "\n" ); document.write( "Consider these two statements :\r
\n" ); document.write( "\n" ); document.write( "(i) If x=2 then x is an even number (TRUE)
\n" ); document.write( "(ii) If x is an even number, then x = 2 (FALSE, x could be 4, 6, 8, 10 etc.)\r
\n" ); document.write( "\n" ); document.write( "So just reversing a satement around does not guarantee that it is equally true. Consider these two statements for example :\r
\n" ); document.write( "\n" ); document.write( "(i) My dog is brown
\n" ); document.write( "(ii) That dog over there is brown so therefore it must be my dog.\r
\n" ); document.write( "\n" ); document.write( "You get the idea ?\r
\n" ); document.write( "\n" ); document.write( "So what is a good converse statment ?
\n" ); document.write( "It IS true to say (assuming the first statement to be always true) : \"If the kitchen does not smell good then you are not baking brownies\". (ANSWER) \n" ); document.write( "

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