ishan

would you really rather choose safe things like. restaurant. or. chocolate. or. idk. whatever

u should post the essay i wanna see

yeah its extremely important in math too

yeah i think its just that i don't consider this a "contradiction of the contrapositive" but i can see how it could be reasonable to. i think i was interpreting contradiction as the implication being false if p.

i agree

i think all i wanted to agree with you on is that contrapositives are equivalent to what they are derived from. like if we are told "if A then B" then whether that person is telling us the truth is exactly the same as whether its true if they say "if Not B then Not A"

okay... unfortunately i am used to thinking of people saying contrapositive of X having to only do with things in X

oh okay i think what you were saying by "contrapositive contradicts the stimulus" is that "first part of contra. contradicts the stimulus"? i think the main confusion is that the truth value of an implication is independent of the truth value of its parts.

are you considering ~X = Not live in Texas to be the "contrapositive" of X = Live in Texas?

I see the issue now. you cannot take the contrapositive of a logical statement. you can do that to implications. you can apply "contrapositive" to a statement like X = "if you have a square you have a rectangle". the only thing you could do to X = Live in Texas is negate it.

i think we may be misunderstanding what the other means by "contrapositive". i am talking about things in a very precise mathematical sense

if you don't, i would be curious how you define contrapositive. here is mine let x and y be logical statements that are true or false. let (x -> y) be true when x being true means y must be true then the contrapositive is the statement (~y -> ~x) and is always equal to (x -> y)

i agree, and in fact one step further: X contradicts Y. do you agree?

what i hope to convey is: if you say "the contrapositive of X contradicts Y" then you must say "X contradicts Y" you seem to be saying that "the contrapositive of X contradicts Y" implies "X does not contradict Y", which is wrong. please correct any mischaracterization.

u claim: (p -> q) = D (p -> q) = (~q -> ~p) (contrapositives are equiv.) but then you claim (~q -> ~p) != second sentence therefore, D = (p -> q) != second sentence. therefore, D does not follow from that sentence. i have tried to only use ur logic. what have i done wrong?

if it is still not clear what point I am making, please oblige me and define what "p" and "q" are that you are taking the contrapositive of!

yeah, your example demonstrates my point that the truth of the original is the same as the truth of the contrapositive. but you claim the contrapositive contradicts the commenter's sentence, and if that is correct, necessarily the original must contradict it too

yes, and we know the contrapositive (~q -> ~p) is equivalent to the original (p -> q). for example, let p = "u have a square" and q = "u have a rectangle" both statements are then true: if u have square u have rectangle, and if you do not have rectangle u do not have square

are you sure you mean contrapositive? p -> q is equivalent to ~q -> ~p which is what’s called the contrapositive. the truth of either implies the truth of the other, so if the contrapositive contradicts something, so does the original. you seem to be talking about the inverse.

final year of college does feel different. its like life tutorial mode is ending. we used to worry about exams and scores and we picked our next actions from a small set but now you are free to do anything which is so scarily broad. feels weird.

AWWWWW hi michael mac and arielle