conditional statements

[logistic_guy]

Write each of these statements in the form “if \(\displaystyle p\), then \(\displaystyle q\)” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]

\(\displaystyle \bold{a)}\) I will remember to send you the address only if you send me an e-mail message.
\(\displaystyle \bold{b)}\) To be a citizen of this country, it is sufficient that you were born in the United States.
\(\displaystyle \bold{c)}\) If you keep your textbook, it will be a useful reference in your future courses.
\(\displaystyle \bold{d)}\) The Red Wings will win the Stanley Cup if their goalie plays well.
\(\displaystyle \bold{e)}\) That you get the job implies that you had the best credentials.
\(\displaystyle \bold{f)}\) The beach erodes whenever there is a storm.
\(\displaystyle \bold{g)}\) It is necessary to have a valid password to log on to the server.
\(\displaystyle \bold{h)}\) You will reach the summit unless you begin your climb too late.

 

[khansaheb]

Write each of these statements in the form “if \(\displaystyle p\), then \(\displaystyle q\)” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]

\(\displaystyle \bold{a)}\) I will remember to send you the address only if you send me an e-mail message.
\(\displaystyle \bold{b)}\) To be a citizen of this country, it is sufficient that you were born in the United States.
\(\displaystyle \bold{c)}\) If you keep your textbook, it will be a useful reference in your future courses.
\(\displaystyle \bold{d)}\) The Red Wings will win the Stanley Cup if their goalie plays well.
\(\displaystyle \bold{e)}\) That you get the job implies that you had the best credentials.
\(\displaystyle \bold{f)}\) The beach erodes whenever there is a storm.
\(\displaystyle \bold{g)}\) It is necessary to have a valid password to log on to the server.
\(\displaystyle \bold{h)}\) You will reach the summit unless you begin your climb too late.

show us your effort/s to solve this problem.

 

[logistic_guy]

Let us try to crack \(\displaystyle \bold{a)}\).

\(\displaystyle p \rightarrow \) I will remember to send you the address
\(\displaystyle q \rightarrow \) you send me an e-mail message

It does not make sense to write:

If I will remember to send you the address, then you send me an e-mail message.

But it makes sense to reverse:

If you send me an e-mail message, then I will remember to send you the address.

But if you reverse, you're violating the rule “if \(\displaystyle p\), then \(\displaystyle q\)”. Technically, you're using “if \(\displaystyle q\), then \(\displaystyle p\)”.

So, what do you think professors? Is reversing considered a valid excuse in this case?

 

[pka]

You need a basis logic text!
P is: I will remember to send you the address
Q is : you send me an e-mail message
P only if Q is equivalent to if P then Q

 

[Steven G]

First makes post with no work shown and then posts the solution. This is in violation of the posting guidelines.
Reported this OP to the admin---again

 

[logistic_guy]

You need a basis logic text!
P is: I will remember to send you the address
Q is : you send me an e-mail message
P only if Q is equivalent to if P then Q

In a logic sense, yes it is, but it seems it does not fit precisely in every English sentence unless you switch the order or rephrase it which will change the meaning slightly.

 

[pka]

In a logic sense, yes it is, but it seems it does not fit precisely in every English sentence unless you switch the order or rephrase it which will change the meaning slightly.

That is nonsense!
I will remember to send you the address only if you send me an e-mail message.
If I remember to send you the address then you have send me an e-mail message.

 

[logistic_guy]

If I remember to send you the address then you have send me an e-mail message.

Your sentence implies that your remembering to send the address is the cause, and the e-mail message being sent by the other person is the result. This suggests a reverse relationship compared to the original sentence.

 

[laucha54321]

Dating for Sex.

Best realistic sex game

 

[logistic_guy]

\(\displaystyle \bold{b)}\) If you were born in the United States, then you are a citizen of this country.

 

[logistic_guy]

\(\displaystyle \bold{c)}\) If you keep your textbook, then it will be a useful reference in your future courses.

 

[The Highlander]

\(\displaystyle \bold{b)}\) If you were born in the United States, then you are a citizen of this country.

No, I would argue it should be:-

b) If you were born in the United States then you meet the sole criterion necessary to be a citizen of that country.​

 

[logistic_guy]

No, I would argue it should be:-

b) If you were born in the United States then you meet the sole criterion necessary to be a citizen of that country.​

Appreciate your interferenceyour sentence implies that there are no other possible criteria for citizenship at all than to be born there. If I were you I would omit the word \(\displaystyle \text{sole}\).

It would be more fun if you have the guts to tell every student (which sounds impossible) why the sentence of professor pka in post #7 is wrong!

 

[Dr.Peterson]

I've been ignoring this, but there's too much that needs saying.

It would be more fun if you have the guts to tell every student (which sounds impossible) why the sentence of professor pka in post #7 is wrong!

But it is not. He's right:

I will remember to send you the address only if you send me an e-mail message.
If I remember to send you the address then you have sent me an e-mail message.

You say,

It does not make sense to write:

If I will remember to send you the address, then you send me an e-mail message.​

But it makes sense to reverse:

If you send me an e-mail message, then I will remember to send you the address.​

But if you reverse, you're violating the rule “if \(\displaystyle p\), then \(\displaystyle q\)”. Technically, you're using “if \(\displaystyle q\), then \(\displaystyle p\)”.

This is incorrect. You've actually written the converse, not an equivalent statement.

In a logic sense, yes it is, but it seems it does not fit precisely in every English sentence unless you switch the order or rephrase it which will change the meaning slightly.

Yes, it's weird; but changing the order produces the converse, not a sensible equivalent.

This problem (which does not belong in "Pre-algebra", but in Logic) is not about ordinary language, but about logical operators, which have precise definitions. Nor are they about real life at all. (And a statement does not have to be true to be written!)

The weirdness is because details like tense are ignored. More literally, we would convert

"I will remember to send you the address only if you send me an e-mail message"​

to

"If I will remember to send you the address, then you send me an e-mail message",​

but that is odd English, so we tend to modify tenses to make sense, something like

"If I remember to send you the address, then you will send me an e-mail message".​

The claim is merely that sending the address implies sending the message; it's a promise [by the other person, I suppose!] that if the address is/was/will be sent, then we can be sure that the message is/was/will be sent [to that address]. The original form is a twisted version of that promise that doesn't sound like a promise; only a logician could say it:

"I will remember to send you the address only if you send me an e-mail message"​

means that the only way the address can have been sent is if the message turns out to be sent; it is impossible for the address to be sent without the message being sent.

I sort of wish that logic texts would not go out of their way to make logic look weird, in order to teach students to ignore reality when writing symbolic statements, but they do. I suspect it teaches students to ignore logic, instead.

There's another issue:

Your sentence implies that your remembering to send the address is the cause, and the e-mail message being sent by the other person is the result. This suggests a reverse relationship compared to the original sentence.

Logical conditional statements are not about causality. They are about one thing being true whenever (not because) the other is true.

"p ONLY IF q" is equivalent to "If p THEN q", because in both cases, if you know that p is true, then you know q must be true. The first says that the only way p can be true is if q is true; the second says, equivalently, that whenever p is true, q is true.

 

[Dr.Peterson]

A different issue arises in (b), "To be a citizen of this country, it is sufficient that you were born in the United States."

\(\displaystyle \bold{b)}\) If you were born in the United States, then you are a citizen of this country.

This is correct, in terms of logic.

No, I would argue it should be:-

b) If you were born in the United States then you meet the sole criterion necessary to be a citizen of that country.​

No, this isn't the sort of mere logical restatement they are asking for, so it is not a better answer. You're going beyond the logic, and therefore risking error.

your sentence implies that there are no other possible criteria for citizenship at all than to be born there. If I were you I would omit the word sole.

Actually, it is not really the word "sole" that is wrong! (Though you may have the right idea in mind.)

It is true that sufficiency means nothing more is required, so "sole criterion" is (sort of) appropriate, though it's a little ambiguous, as I'll explain. We have to take it to mean that there is no additional criterion.

In fact, however, the word "necessary" should definitely be removed.

Sufficiency means it is enough (to be born there), not that there is no other way! The given statement does not say that being born there is necessary, so that one must be born there to be a citizen, and there is no alternative criterion. No more is necessary; but something else might also be sufficient.

The original statement would still be true if, say, the law makes you a citizen also if you are born in another country, but to U.S. citizens. (That is true, but its truth is not required in this discussion; and it is also irrelevant that, in fact, one can be born in the U.S. and not be a citizen, if, say, your father was an ambassador of another country. I say this not because it's at all relevant to the logic, but because it's interesting, and currently in the news.)

Anyway, all they want or need is "If you were born in the United States, then you are a citizen of this country."

And the conclusion from all this is that English, even when we try to use it carefully, can't be as precise as logic symbols. And that's true of any human language. We're always implying things we didn't mean to say.

 

[logistic_guy]

Thanks professor Dave for the long explanation. Let me take this fragment and focus on it: you're saying professor pka sentence is correct in post #7. When I said it's wrong I did not meant grammatically, I meant it's not equivalent to the original sentence.

In the original sentence it's necessary to send the email first, but in pka's is the reverse it's necessary to remember first. Therefore, how can it be correct?

The claim is merely that sending the address implies sending the message; it's a promise [by the other person, I suppose!] that if the address is/was/will be sent, then we can be sure that the message is/was/will be sent [to that address].

This is an enough evidence that his sentence is wrong.

 

[Dr.Peterson]

Thanks professor Dave for the long explanation. Let me take this fragment and focus on it: you're saying professor pka sentence is correct in post #7. When I said it's wrong I did not meant grammatically, I meant it's not equivalent to the original sentence.

In the original sentence it's necessary to send the email first, but in pka's is the reverse it's necessary to remember first. Therefore, how can it be correct?


This is an enough evidence that his sentence is wrong.

Please reread what I said. You are utterly missing my point.

I assume you are not studying logic, and have not read about this subject, or you would know that pka's sentence absolutely is equivalent, while yours absolutely is not. Please find a book about logical connectives and read carefully.

 

[logistic_guy]

Please reread what I said. You are utterly missing my point.

Not me who is missing your point. I think that it's you who is missing my point.

I know that in Logic P only if Q is equivalent to if P then Q.
So with Logic
I will remember to send you the address only if you send me an e-mail message.
is equivalent to
If I remember to send you the address then you have send me an e-mail message

without Logic (Here is my main point.)
I will remember to send you the address only if you send me an e-mail message.
is equivalent to
If you send me an e-mail message, then I will remember to send you the address.

Again
With Logic if you have P only if Q, it's the converse to write if Q then P.

Without Logic, it appears for the first sentence it's ok to write if Q then P (And it looks equivalent not the converse).

Conclusion: Forcing everyday English to be written in Logic style does not always make sense Like what happened in the first sentece!

 

[The Highlander]

Appreciate your interferenceyour sentence implies that there are no other possible criteria for citizenship at all than to be born there. If I were you I would omit the word \(\displaystyle \text{sole}\).

It would be more fun if you have the guts to tell every student (which sounds impossible) why the sentence of professor pka in post #7 is wrong!

I take your point but also note that the original sentence says "To be a citizen of this country,..." so it would also be necessary to consider that the speaker/writer might not actually be in the US at the time of speaking/writing but actually in another country altogether, however, a quick Google search convinces me that US citizenship alone would not be sufficient to gain citizenship in any other country.

The intervening posts were TLDR so I would just change my rendition to:-

b) If you were born in the United States then that is sufficient to be a citizen of that country.

or

b) If you were born in the United States then that is all you need to be a citizen of that country.​

Beyond that response, I have totally lost interest.

 

[Dr.Peterson]

Not me who is missing your point. I think that it's you who is missing my point.

I know that in Logic P only if Q is equivalent to if P then Q.
So with Logic
I will remember to send you the address only if you send me an e-mail message.
is equivalent to
If I remember to send you the address then you have send me an e-mail message

without Logic (Here is my main point.)
I will remember to send you the address only if you send me an e-mail message.
is equivalent to
If you send me an e-mail message, then I will remember to send you the address.

But the problem is about logic, so you can't answer without logic; and your answer here is not valid even in ordinary language.

Forgetting the symbolic logic, we can still say that the original statement will not be a lie if I don't remember, but you do send me an email. Am I right?

But you're claimed equivalent statement, "If you send me an e-mail message, then I will remember to send you the address", would be a lie under those conditions.

That's my main point: there is no way your answer can be correct. Of course, outside of logic, we would never make the original statement in the first place!

Again
With Logic if you have P only if Q, it's the converse to write if Q then P.

Without Logic, it appears for the first sentence it's ok to write if Q then P (And it looks equivalent not the converse).

But is is NOT equivalent.

Conclusion: Forcing everyday English to be written in Logic style does not always make sense Like what happened in the first sentece!

This is (sort of) a point I made:

I sort of wish that logic texts would not go out of their way to make logic look weird, in order to teach students to ignore reality when writing symbolic statements, but they do. I suspect it teaches students to ignore logic, instead.

It doesn't make sense in ordinary language; but that is mostly because of the tenses, not the meaning.