I am particularly confused at the the difference(s) when translating conditional statements into english. For instance the statements below from a question I found online. I will go to the movie if I complete my assignment. I will go to the movie only if I complete my assignment. I will not go to the movie if I do not complete my assignment.  I understand the differences between the first two in simple english, but how can I express this in propositional logic using the conditional (or bi-conditional) arrows?
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For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpret this is, "It is true that Samir will attend the party only if it is true that Kanti will be at the party;" which, in my mind, becomes "If Kanti will be at the party, then Samir will be there."   Can someone convince me of the right way?  EDIT:  I have read them carefully, and probably have done so for over a year. I understand what sufficient conditions and necessary conditions are. I understand the conditional relationship in almost all of its forms, except the form "q only if p." What I do not understand is, why is p the necessary condition and q the sufficient condition. I am not asking, what are the sufficient and necessary conditions, rather, I am asking why.
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I just wonder if the two following sentences are truth-conditionally the same. Sentence 1 essentially means there existed a student who entered the room, and this situation includes two, three or more students entering the room. Hence, I believe these two sentences are truth-conditionally the same. Are they?        A student entered the room.   At least one student entered the room.      How about        One student entered the room      I gather this is different, as sentence 3 only means one student, not more and not fewer?  Any and all insights would be welcome.
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What's the difference between  and  ?
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I have a ques­tion re­gard­ing con­di­tional sen­tences, as far I know the “third con­di­tional” is used when we’re talk­ing about a con­di­tion from the past that never ac­tu­ally hap­pened af­ter all.  For ex­am­ple:  If she had come home early, she would have got­ten to meet him.  In this ex­am­ple, the per­son did ɴᴏᴛ get home early so she did ɴᴏᴛ get to see whomever she had been want­ing to see. But what about the cases where it’s un­cer­tain whether that if clause’s con­di­tion had ever ended up getting fulfilled or not? If in the ex­am­ple sen­tence it had ɴᴏᴛ been known whether she had come home early — maybe she did, maybe she didn’t, but we don’t know — what then would have been used in place of If she had come home early, given how that par­tic­u­lar con­struc­tion would clearly im­ply that she had ɴᴏᴛ come home early and we want to al­low for doubt about that?
94627
Sometimes I hear sentences that sound conditional to me, just because of the (unassertive) ordering of the words. I don't know if I can come up with a proper example. Consider this:          I'd be a lot better, had she stayed with me.        And I guess it's equivalent to this conditional form: If she had stayed with me, I would have been a lot better.  So, this is my question: In what ways can you make a sentence conditional without using conditional conjunctions (if, unless, etc)? And what are their equivalent conditional forms?
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I have been taught to use the if I had form in conditional clauses referring to the past:     If the president had asked me, I would have told him the same thing.   As far as I can tell though, the would have construct is sometimes used in conditional clauses as well, so it wouldn't be incorrect to say:     If the president would have asked me, I would have told him the same thing.   What is the difference between the two and the proper use of the latter?
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If she be found guilty… ()   I got a curiosity what difference there is when I put ‘is’ instead of ‘be.’ The dictionary says ‘is’ is used in spoken language. Is that all? Is there no semantic difference at all?
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In many languages assignments are legal in conditions. I never understood the reason behind this. Why would you write:  if (var1 = var2) {   ... }   instead of:  var1 = var2; if (var1) {   ... }
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When translating English phrases to mathematical statements using logical quantifiers, I find that I'm having trouble knowing the difference between $P(x)\wedge Q(x)$ and $P(x)\to Q(x)$.  For example:  Translate the following sentences using logical quantifiers:   All rationals are real No rationals are real Some rationals are real Some reals are rational   My notes say the following:   $Q(x)$: $x$ is rational $R(x)$: $x$ is real   All rationals are real: $(\forall x)(Q(x)\to R(x))$ No rationals re rel: $(\forall x)(Q(x)\to\neg R(x))$ Some rationals are real: $(\exists x)(Q(x)\wedge R(x))$ Some reals are rational: $(\exists x)(R(x)\wedge Q(x))$    So I have to wonder: Why, for number 1 and 2 is it not right to say $(\forall x)(Q(x)\wedge R(x))$? I've gotten many questions like this wrong because I said $A\to B$ when it was supposed to be $A\wedge B$.
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I'm not a native speaker. Apologies if the question is obvious.  The scenario is:   I'm not doing A, and I'm not doing B.   In order to communicate this joint event in a single sentence: should I say: "I'm not doing A or B" or "I'm not doing A and B." (I know I can also say "I'm doing neither A nor B" but that is a seperate solution.)  The source of my uncertainty is that the logical negation of (A and B) is [(not A) or (not B)] so I don't know whether "I'm not doing A and B" can be interpreted as   I'm not doing A, or I'm not doing B.   which is not my original scenario.
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I am asking here specifically about if and whether  when they introduce embedded questions (or to be more technically accurate, subordinate interrogative clauses):  I don't know if Bob's here. I don't know whether Bob's here.  In the sentence above we can freely replace if with whether. There are some situations in which the reverse does not apply. We cannot always replace whether with if. For example in standard English, we cannot normally use if after a preposition:  The question of whether he is actually eligible didn't arise. *The question of if he is actually eligible didn't arise.  We cannot usually use interrogative-if directly followed by or not:  It's unclear whether or not he's a real elephant. *It's unclear if or not he's a real elephant.  There are several more examples. However, what I want to know is:  Are there any examples where we can use interrogative-if but we can't use whether?   Edit note: There is an if that we find in conditionals that can't be replaced by whether. However, this is conditional, not interrogative, if.
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As a nonnative speaker of English I was always taught in school that there are verbs that cannot be used in the continuous form, i.e.  the stative verbs. However, I've seen some stative verbs used in the continuous form in American English, especially the verbs wish, feel, hope, guess, love and like. Is using these stative verbs in the continuous form wrong? If it's not, what's the difference between using them in the simple and continuous forms?
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“There are open fields over there,” he said, pointing, “in case it happens.”  “There are open fields over there,” he said, pointing, “if it happens.”    Are &quot;if&quot; and &quot;in case&quot; generally interchangeable? If not, how is 1, the original version, different from 2?
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My book and my teacher both said that these two statements are different:  1) $∀x∈A,∃y∈B, F(x, y)⇒G(x)$  2) $∀x∈A,(∃y∈B, F(x, y))⇒G(x)$  How can just adding an extra parenthesis make the statement different? I am not quite sure I understand.  If they are different, how are there negation different? Would the negation be as follows:  1) $∀x∈A,∃y∈B, F(x, y) ∧ ¬ G(x)$  2) $∀x∈A,(∀y∈B, ¬ F(x, y)) ∧ ¬ G(x)$    SIDE NOTE: I tried taking contrapositives, but ended up with the same expression for both. So how and why are they diffrent? $¬ G(x) ⇒ ∃x∈A,∀y∈B, ¬ F(x, y) $    Thanks
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Here are two sentences. 1. What are you doing in here? 2. What are you doing here?  What is the difference between the two sentences? (between No,1 and No,2 sentences)  Is there any grammar to omit preposition like above?
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When we say,      It is not fair.   or     It is unfair.   I'm not sure enough to say whether both of the sentences have the same meaning or not though superficially, there is no difference between them but if we say,     Something is not possible.   or     Something is impossible.   then there is really an observable difference in my first language. Hence, the question - is there a difference between the preceding two sentences in English?
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Implication does not appear to be associative:  a  b  c | (a -&gt; b) -&gt; c | a -&gt; (b -&gt; c) F  T  F | F             | T F  F  F | F             | T   Is $a \implies b \implies c$ evaluated as $a \implies (b \implies c)$ or $(a \implies b) \implies c$?