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The question below consists of a main statement followed by four options. From the options, select the one that logically follows the main statement.

Statement: Either I give up or I work hard.

(A) I am not going to give up, hence I will work hard.

(B) I am not going to work hard, therefore I’ll give up.

(C) I’ll give up, still, I’ll keep on working hard.

(D) Both (A) and (B)

I think all three statements (A, B and C) follow the main statement because the "or" operator gives "True" value for all the cases except when both statements are false.

Also, I am confused about what does "logically follows" mean?

Aman Goyal
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    What do you think and why? – Doug Spoonwood Aug 22 '20 at 14:18
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  • @DougSpoonwood please check now. – Aman Goyal Aug 22 '20 at 14:30
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    None of those four follows from what's given. – David C. Ullrich Aug 22 '20 at 15:00
  • If (C) were correct, then "I'll give up" would have to come as necessarily true. But, it could false. Thus, (C) can't be correct. I don't know exactly the meaning getting ascribed to "hence" and "therefore". I'm tempted to think of them as synonymous, in which case (C) will end up as the best answer (though usually "hence" and "therefore", don't have the same meaning as "if ... then ..."). However, if they don't, then (A) or (B) uniquely may hold. – Doug Spoonwood Aug 22 '20 at 21:49

1 Answers1

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The language used here is not what I am accustomed to. I usually see someone write that $P$ follows from $Q,$ not that "$P$ follows $Q$" without the word "from".

There is also some weirdness in the use of tenses here. If I am working hard at this moment, but I will not work hard in the future, is "I work hard" true or false?

But let's suppose that either all the "work hard" clauses are true or all are false, and likewise with the "give up" clauses. (If we do not make this assumption then I do not think we can relate the main statement, with clauses in the present tense, to any of the other statements, with clauses in the future tense.)

Note that in (A) I work hard and I do not give up; in (B) I give up and I do not work hard; in (C) I give up and I work hard.

Then here is a truth table:

\begin{array}{cccccc} \text{work hard} & \text{give up} & \text{main} & \text{A} & \text{B} & \text{C} \\ F & F & F & F & F & F \\ F & T & T & F & T & F \\ T & F & T & T & F & F \\ T & T & T & F & F & T \\ \end{array}

So let $Q$ be the main statement. When we write that $P$ follows from $Q,$ we mean that in all worlds in which $Q$ is true (that is, all rows of the table with a $T$ under "main"), $P$ also is true (that is, there is a $T$ under the heading for $P$). But for each of the headings A, B, and C, there are two rows in which the main statement is true but the other statement is false. Hence none of these statements follows from the main statement.

Check your post for transcription errors. Did you copy the question faithfully? If so, I think the source you got it from is badly flawed.

David K
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  • I don't see the use in this answer, since one of the four has to work out as the "best answer" by supposition of the question. "If I do not give up, then I'll work hard" holds true when "main" holds true, and I think that "A" means that. "If I'm not going to work hard, then I'll give up" holds true when "main" holds true, and I believe that "B" got intended to mean that. – Doug Spoonwood Aug 22 '20 at 21:59
  • @DougSpoonwood "If I do not give up, then I'll work hard" is exactly equivalent to "I will give up or I will work hard"; $X\implies Y$ is equivalent to $\lnot X\lor Y.$ But one way to satisfy "If I do not give up, then I'll work hard" is to give up and not work hard. I cannot see how someone who gives up and does not work hard has made it true that "I am not going to give up, hence I will work hard." That statement does follow from the conjunction of the main statement together with the statement "I will not give up," but not from the main statement alone. – David K Aug 22 '20 at 22:09
  • @DougSpoonwood Why do you completely discount the possibilities raised in the last paragraph of the answer? It is logically possible for someone to write a multiple-choice question in which all choices are incorrect. All it requires is for them to make a mistake. – David K Aug 22 '20 at 22:11
  • I don't discount the possibility that no answer will be correct for some multiple choice given on some sort of test or assignment. However, I don't see how if one is given a question which says: "From the options ....", how an answer discounting all of the provided answers is useful to answering such a question, since it doesn't have an answer that is one of the options. – Doug Spoonwood Aug 22 '20 at 22:28
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    @DougSpoonwood I think "the book you're reading is crap" is a useful thing for someone to know. – David K Aug 22 '20 at 22:38
  • Also consider that this is not a do-my-homework site. If the answer to the question actually had been one of the choices, I probably would not have written an answer. (I might have commented to prod the asker to answer their own question.) – David K Aug 22 '20 at 22:41
  • @DougSpoonwood I can't see how you're making any sense. If all the answers are wrong there is no best answer. – David C. Ullrich Aug 22 '20 at 23:00