Necessary and Sufficient Conditions
In Epstein's book it states that two claims are equivalent if both claims are true exactly when the other one is. This can be seen in a contrapositive sentence. A contrapositive sentence is if A is true then so is B, if B is not true then A is not true either. A claim and its contrapositive are alway the same. An example of this is the contrapositive of "if it is raining the the ground will be wet" is "if the ground is not wet then it is not raining." In the example the contrapositive of any true proposition is also true.
The Contradictory of A Claim
In the book it states that any compound claims are claims that are made up from other types of claims but can only be seen as one claim instead of many claims. It can get confusing to see if these type of claims are false, so a contradictory of a claim is the opposite of the original claim. An example of this type of claim is that "Tony went to the dining commons" while the contradictory or the opposite would be "Tony did not go to the dining commons."
I also talked about the contradictory of a claim which in most cases states the opposite from the truth or original claim. I didn't know what a contradictory claim was until I read the section on Chapter 6. Epstein states the definition of a contradictory claim, but at first it left me confuse because I didn't completely understand the definition. Then I saw examples on pp. 114 on claims and their contradictory claims which made more sense. Yes I agree with you the contradictory claim is just the opposite of the claim to put it into more simple terms. I like the example you use to show what a contradictory claim is.
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ReplyDeleteHello,
ReplyDeleteYour description of necessary and sufficient conditions was very clear and it helped me understand this concept better.
You really condensed the information when you stated "A claim and its contrapositive are always the same." I noted this so that it would be easier for me to decipher if my or another person's claim and its contrapositive are interrelated.
I would like to share a claim and contrapositive of my own:
Claim: "If the sun is out, then Gate will get a sunburn."
Contrapositive: "If the Gate does not get a sunburn, then the sun is not out."
Thanks for posting about necessary and sufficient conditions, it really clear up the confusions I had with concept.