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keebler01
Group Title
Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion.
I) If the cat does not have claws, then the cat cannot scratch the furniture.
II) If the cat can scratch the furniture, then the cat has claws.
III) If the cat has claws, then the cat can scratch the furniture.
a. I and II are equivalent
b. I and III are equivalent
c. II and III are equivalent
d. I, II, and III are equivalent
e. None are equivalent
 3 years ago
 3 years ago
keebler01 Group Title
Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. I) If the cat does not have claws, then the cat cannot scratch the furniture. II) If the cat can scratch the furniture, then the cat has claws. III) If the cat has claws, then the cat can scratch the furniture. a. I and II are equivalent b. I and III are equivalent c. II and III are equivalent d. I, II, and III are equivalent e. None are equivalent
 3 years ago
 3 years ago

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saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
this is hard.
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
The first thing you need to do is transform these statements into statements using propositional logic: \[p = \text{cat has claws}\]\[q = \text{cat can scratch furniture}\] 1) \(\neg p \implies \neg q\) 2) \(q \implies p\) 3) \(p \implies q\) Since 1 & 2 are contrapositions of each other, therefore they are logically equivalent. However 3 is not equivalent to 1 or 2. Therefore I would say the answer is \(a\)
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
To be more specific the converse of a statement is not logically equivalent to the statement.
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
So to be clear p>q does not imply q>p
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
Do you understand?
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
heck no!!!
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
saifoo not funny!
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
Here, I will explain. Lets look at these two statements: \[p=\text{"it is raining"}\]\[q=\text{"i am getting wet"}\] Suppose \(p \implies q\) If it is raining, then I am getting wet. Is that the same as \(q \implies p\)? If I am getting wet then it is raining. The answer is clearly no. Do you understand so far?
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
You could be getting wet, even when it is not raining (shower for instance).
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
saifoo not funny!
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
okay i get that part!
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
So we've established that \(p \implies q\) does not necessarily mean \(q \implies p\). However, as I have stated before. I have made the claim that if \(p \implies q\) then \(\neg q \implies \neg p\). So \(p \implies q\) is If it is raining then I am getting wet. Is that the same as \(\neg q \implies \neg p\) If I am not getting wet, then it is not raining. Well we have stated that if it is raining then I am getting wet. So if I am not getting wet then it is not raining, or the first implication would not hold. Do you see how these two are logically equivalent?
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
yes i understand now!
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
So now apply this to the original problem. Do you see how only the first two statements about the cat are logically equivalent?
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
saifoo not funny!
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
so what is my awser
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
Well look at the choices. What do you think is the correct answer?
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
A sound reasonable!
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
Yes, A is the correct answer.
 3 years ago

keebler01 Group TitleBest ResponseYou've already chosen the best response.0
so how wouldi right this!
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
I suggest you read about contrapositive and converse statements.
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
Once you fully understand those two concepts, it will be immediately clear that only 1 & 2 are equivalent.
 3 years ago

Alchemista Group TitleBest ResponseYou've already chosen the best response.1
http://en.wikipedia.org/wiki/Contraposition http://en.wikipedia.org/wiki/Conversion_(logic)
 3 years ago
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