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# what is the negation of "Either he will do it on time, or he won't get paid" ?

11 Answers

+ 9

The negation is: "He will not do it on time and he will get paid."
Edit:
This answer assumes that "either or" is an inclusive or.
On the other hand, if "either or" is interpreted as an exclusive or, then the negation is: "He will do it on time and won't get paid ... or... he will not do it on time and he will get paid." This is an if and only if situation.
Some people may also interpret the original statement to mean: Either he will do it on time, or ELSE (otherwise) he won't get paid. This is an "A implies B" situation which is semantically equivalent to "If he doesn't do it on time, he won't get paid." In this case, the negation is: "He doesn't do it on time and he will get paid."
As can be seen, the inexactness of natural language can lead to different semantic interpretations.

+ 7

Bennett Post suppose that:
Preposition A = "He will do it on time"
Preposition B = "He won't get paid"
The original statement, therefore is: (A or B)
The negation is: !(A or B)
which is equivalent to: (!A and !B)
which is what I said.

+ 7

The statement is he will do it in time AND he will be paid.
Negation is he will not do it in time AND NOT get paid.

+ 6

I have taken "either or" in English to mean an inclusive or, not an exclusive or. But I see that doubt about this is what can cause confusion here. I have added an explanation to my original answer.

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Bennett Post Sonic
Actually, I think neither of you are(n't) wrong. When the standalone statement "Either p or q" is uttered in this context, the teller is implying that only one of the two variables can be true, and the other one must be false. p and q cannot be both true, and also cannot be both false. This is actually, the XOR operator is play. When you look at it, Bennett's truth table is accurate (with the negation of q).
https://english.stackexchange.com/questions/13889/does-either-a-or-b-preclude-both-a-and-b
"Either A or B" most precisely means, in symbolic logic terms, "AÂ XORÂ B", while "A OR B" is expressed as "A or B" or the extensive "Either A, or B, or both".
The negation of XOR, which only outputs true when both variables are the same, is known as the logical biconditional.
https://en.m.wikipedia.org/wiki/Logical_biconditional
I propose the direct negation of the statement, based on the logic above, to be
"He will do it on time, if and only if he won't get paid."

+ 2

hls @hl no, check sonic answer

+ 2

Bennett Post
maybe it's strange negation, but from a cs view point this is the negation for that sentence.

+ 2

if u say he will not do it, and then will not paid, it is the same meaning, not the negation.

+ 2

sonicâs answer obeys de Morgans rule, try making a truth table if you get stuck

+ 1

He will do it in the time it takes to do it AND he will get money for it.

0

He will get paid if he can finish it on time