Thursday, March 10, 2011
Contrapositives
In Chapter 6, I learned about the two claims that are both equivalent only if they are both TRUE. This is the necessary and sufficient conditions of a contra-positive claim. Contra-positive statements is when the claim and contra-positive are similar to each other. If the original proposition is true, then the contra-positive is true as well. For example, "All dishes have to be washed." --> "If you use the dishes to eat, you must wash them after." (if A, then B). If the proposition is false, then the contra-positive is false as well. A necessary condition of a claim is when A is necessary for B meaning if "If you do not pass English 1B, then you cannot enroll in English 1B." On the other hand, a sufficient condition is when A is sufficient for B. An example of this is "If you are a stranger and you touch me, I will scream because I do not know you."
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Impressive! I think reading this blog made it easier to understand rather than having to read the section in the book about this topic! I was wondering if there was a term or concept for that “if A, then B”, and I guess there is! I thought the contra-positive explanation was great and clearly explained. Hmm, do you mean if you don't pass English 1A in your necessary condition of a claim? I also thought your final example of a stranger touching you, you will scream was hilarious and it also helps explain your contra-positive claim even better!
ReplyDeleteI got lost on the last two examples... The one about English 1B and the creepy molesting stranger. If I don't pass English 1B, then I can't enroll in English 1B? How come? Shouldn't it be: If I don't pass English 1A, then I can't enroll in English 1B? Because we have to finish English 1A first right? English 1A is a prerequisite for English 1B. I'm confused. Haha. And the creepy molesting stranger was scary, but I got kind of confused. I cannot see how that fits into contrapositive. Better go reread the chapter. LOL. I don't see an "If...,then.." clause or an "OR" or anything. Oh wait, maybe if you change it to: If you touch me and I don't know you, then I will scream. Does that work better?
ReplyDeleteOops typo! I meant to say English 1A :)
ReplyDeleteI liked the example that you used because it is something I can tie in with my own personal experiences with the San Jose State parking garages. One day I was in a rush and forgot to buy a ticket, thus I was given a ticket. Like I have said from other posts on this same subject, it really is amazing how much "If A then B" and "If not B then not A" can apply to pretty much anything in real life. Seeing the contra-positive can help you see the consequences a lot better, which would have helped me a lot in my case if I took a second to think about it.
ReplyDeleteI really like how well you always explain your subject of text in your posts. The example you used was very easy to understand and follow. It is nice when people can explain the material better than the book itself that way I can actually learn and understand the material. I feel like I am going to come visit your blog a lot more often! I like your subject you picked to talk about because I was way over my head when reading it in the book. GOOOD JOB! :)
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