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."
Answer by doctor_who(15)   (Show Source):
You can put this solution on YOUR website! No, not necessarily. The kitchen might smell good because you are roasting some coffee.
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.
Consider these two statements :
(i) If x=2 then x is an even number (TRUE)
(ii) If x is an even number, then x = 2 (FALSE, x could be 4, 6, 8, 10 etc.)
So just reversing a satement around does not guarantee that it is equally true. Consider these two statements for example :
(i) My dog is brown
(ii) That dog over there is brown so therefore it must be my dog.
You get the idea ?
So what is a good converse statment ?
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)
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