[logic] true and false statement exercise

[Anne B]

http://discrete.openmathbooks.org/dmoi3/sec_intro-statements.html

> Example 0.2.3. Decide which of the following statements are true and which are false. Briefly explain.

The below questions are not direct copy/pastes because I couldn’t get
that to work right. I could have messed up the quotations.

> 1. If 1 = 1, then most horses have 4 legs.

The “if” part and the “then” part are both true. So the statement is true.

> 2. If 0=1, then 1=1.

This is true. Because the “if” part is false, it doesn’t matter
whether the “then” part is true or false.

> 3. If 8 is a prime number, then the 7624th digit of π is an 8.

This is true for the same reason as the previous one. The “if” part is
false, so I don’t need to try to find out if the “then” part is true
or false.

> 4. If the 7624th digit of π is an 8, then 2+2=4.

This is true. The “then” part is true, so the whole thing is true
whether the “if” part is true or false.

In the solution, they use fancier words. I should get used to using
those words. They call the “if” part the *hypothesis* and the “then”
part the *conclusion*. Both parts put together are called an
*implication*. An *implication* is a kind of *statement* that has a
*hypothesis* and a *conclusion*.

[peter griffin]

I actually understood it better when you used "if part" and "then
part". It's clearer what you're referring to, even if it might sound a
little ungainly in conversation.

[Anne B]

Yeah. It's good to be able to explain things both ways: in everyday
language and in Logic language.

[Alisa Zinov'yevna Rosenbaum]

On Sat, Oct 26, 2019 at 2:25 AM Anne B wrote:

> http://discrete.openmathbooks.org/dmoi3/sec_intro-statements.html
>
>> Example 0.2.3. Decide which of the following statements are true and which are false. Briefly explain.
>
> The below questions are not direct copy/pastes because I couldn’t get
> that to work right. I could have messed up the quotations.
>
>> 1. If 1 = 1, then most horses have 4 legs.
>
> The “if” part and the “then” part are both true. So the statement is true.

This could be expressed more simply as: The “then” part is true. So the statement is true.

(You expressed it that way on (4)).

>> 2. If 0=1, then 1=1.
>
> This is true. Because the “if” part is false, it doesn’t matter whether the “then” part is true or false.

Yes. Alternatively, the "then" part is true, so the entire statement is true (for the same reason as (1)).

>> 3. If 8 is a prime number, then the 7624th digit of π is an 8.
>
> This is true for the same reason as the previous one. The “if” part is false, so I don’t need to try to find out if the “then” part is true or false.

Yes.

>> 4. If the 7624th digit of π is an 8, then 2+2=4.
>
> This is true. The “then” part is true, so the whole thing is true whether the “if” part is true or false.

Yes.

> In the solution, they use fancier words. I should get used to using those words. They call the “if” part the *hypothesis* and the “then” part the *conclusion*. Both parts put together are called an *implication*. An *implication* is a kind of *statement* that has a *hypothesis* and a *conclusion*.

There's also "antecedent" and "consequent": https://en.wikipedia.org/wiki/Antecedent_%28logic%29

I prefer your terminology ("if" part and "then" part).

[Alisa Zinov'yevna Rosenbaum]

On Sat, Oct 26, 2019 at 8:55 AM Anne B wrote:

> On Sat, Oct 26, 2019 at 4:57 AM peter griffin wrote:

>> On Fri, Oct 25, 2019 at 11:25 PM Anne B wrote:

>>> This is true. The “then” part is true, so the whole thing is true whether the “if” part is true or false.
>>>
>>> In the solution, they use fancier words. I should get used to using those words. They call the “if” part the *hypothesis* and the “then” part the *conclusion*. Both parts put together are called an *implication*. An *implication* is a kind of *statement* that has a *hypothesis* and a *conclusion*.
>>
>> I actually understood it better when you used "if part" and "then part". It's clearer what you're referring to, even if it might sound a little ungainly in conversation.
>
> Yeah. It's good to be able to explain things both ways: in everyday language and in Logic language.

You wrote "Yeah" as if you were agreeing with peter, but your next statement seems to me to disagree with him.

IIUC, peter was praising the "if"-part/"then"-part terminology. He criticized the fancier terms by implication (he understood them less well, and they were less clear). But you said it was good to be able to use both.

*Understanding* fancy words has some benefits, but why *use* them yourself when simpler equivalents are available?

[Anne B]

On Oct 26, 2019, at 11:52 AM, Alisa Zinov'yevna Rosenbaum <petrogradp...@gmail.com> wrote:

> On Sat, Oct 26, 2019 at 8:55 AM Anne B wrote:
>
>> On Sat, Oct 26, 2019 at 4:57 AM peter griffin wrote:
>
>>> On Fri, Oct 25, 2019 at 11:25 PM Anne B wrote:
>
>>>> This is true. The “then” part is true, so the whole thing is true whether the “if” part is true or false.
>>>>
>>>> In the solution, they use fancier words. I should get used to using those words. They call the “if” part the *hypothesis* and the “then” part the *conclusion*. Both parts put together are called an *implication*. An *implication* is a kind of *statement* that has a *hypothesis* and a *conclusion*.
>>>
>>> I actually understood it better when you used "if part" and "then part". It's clearer what you're referring to, even if it might sound a little ungainly in conversation.
>>
>> Yeah. It's good to be able to explain things both ways: in everyday language and in Logic language.
>
> You wrote "Yeah" as if you were agreeing with peter, but your next statement seems to me to disagree with him.

Good point.

> IIUC, peter was praising the "if"-part/"then"-part terminology. He criticized the fancier terms by implication (he understood them less well, and they were less clear). But you said it was good to be able to use both.
>
> *Understanding* fancy words has some benefits, but why *use* them yourself when simpler equivalents are available?

Good point. I can’t think of a good reason to use the fancier terms. I’d use them in an academic setting where I wanted to impress people, but I don’t expect to find myself in that situation. I now agree with you that it’s good to understand the fancier terms but use the simpler terms.