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Monday, March 27, 2006
Interesting..
"If Jody doesn't pay her ticket, she will go to jail." Which other statement must be true? If Jody pays her ticket, she won't go to jail. If Jody goes to jail, she didn't pay her ticket. If Jody doesn't go to jail, she paid her ticket.
Very adorable question I found online on some quiz...here's the technical explanation of it The three most common ways to change a conditional statement are by taking its inverse , its converse, or it contrapositive. In each case, either the hypothesis and the conclusion switch places, or a statement is replaced by its negation.
The inverse of a conditional statement is arrived at by replacing the hypothesis and the conclusion with their negations. If a statement reads, "The vertex of an inscribed angle is on a circle", then the inverse of this statement is "The vertex of an angle that is not an inscribed angle is not on a circle." Both the hypothesis and the conclusion were negated. If the original statement reads "if j, then k", the inverse reads, "if not j, then not k." and etc etc but that wasn't the first thing to go running (or limping) through my mind..It was more straightforward:
Statement 1: If she pays her ticket she wont go to jail. not true an assumption because she might have done something else
Statement 2:If she goes to jail, she didn't pay her ticket. Also not true, same explanation as above except she got caught for whatever it is she did do (like run over the guy who issued the ticket)
Statement 3 is true!! because it eliminates any other illegal activities she might Not ( haha roundabout thinking) have done plus this scenario as well. guess it seems pretty simple but you have to be able to consider alternative scenarios and not get too involved in the qn..