# logic

joe shmo
Posers and Puzzles 01 Jan '13 00:08
1. joe shmo
Strange Egg
01 Jan '13 00:083 edits
I'm reading the book " Logic Made Easy: How to Know When Language Deceives You"
The author brings up a question that large percentage of people answer incorrectly, and tells why they mostly give a certain answer.

I'm not debating what the correct answer to the question is ( that we agree on, i think ).

I bolded the information pertinent to my question

Given:
1. All education majors student teach.
2. Some education majors have double majors.
3. Some mathematics students are education majors.

Which of the following conclusions necessarily follows from 1,2, and 3 above?

A. Some mathematics students have double majors.
B. Some of those with double majors student teach.
C. All student teachers are education majors.
D. All of those with double majors student teach.
E. Not all mathematics students are education majors.

She goes on to say "But, most probably, those erring on this question were seduced by the truth of conclusion C. It may be a true conclusion, but it does not necessarily follow from the given statements."

I say her statement (the above statement) is clearly is false, because given (1), no conclusion can be made as to the state of (C), and she is making a conclusion.

It could be that she simply forgot to use the word "possible" in between "the" and "truth", but I just want some opinions, Whats going on, am I out of line?
2. forkedknight
Defend the Universe
01 Jan '13 01:11
Originally posted by joe shmo
I'm reading the book " Logic Made Easy: How to Know When Language Deceives You"
The author brings up a question that large percentage of people answer incorrectly, and tells why they mostly give a certain answer.

[b]I'm not debating what the correct answer to the question is ( that we agree on, i think ).

I bolded the information pertinent to my ...[text shortened]... "the" and "truth", but I just want some opinions, Whats going on, am I out of line?[/b]
I think she means the real-life truth of statement C. People may (partially) ignore the givens in the question and just base their answer on what their own experience is.

In the real world, I can't think of a reason why a student teacher wouldn't be an education major, so it very well could be a true statement. It is not, however, the conclusion that you can draw from the given information using logical reasoning.
3. 01 Jan '13 20:483 edits
I think at least 2 of the statements A to E must definitely be true

1. All education majors student teach.
2. Some education majors have double majors.
3. Some mathematics students are education majors.

A. Some mathematics students have double majors. true if E is false, otherwise no evidence for this
B. Some of those with double majors student teach. definitely true because of 1 and 2
C. All student teachers are education majors. true if E is false, otherwise no evidence for this
D. All of those with double majors student teach. no evidence for this
E. Not all mathematics students are education majors. could be true, depending on the weight we give to "some" in 3
4. 03 Jan '13 13:34
sorry, a correction, still at least 2 statements are true though:

1. All education majors student teach.
2. Some education majors have double majors.
3. Some mathematics students are education majors.

A. Some mathematics students have double majors. true if E is false, (because then all mathematics students are ed. majors, and we know some ed. majors have double majors) otherwise no evidence for this

B. Some of those with double majors student teach. definitely true because of 1 and 2

C. All student teachers are education majors. No evidence for this, one of the teachers could be a duck for all we can tell
D. All of those with double majors student teach. no evidence for this
E. Not all mathematics students are education majors. could be true, depending on the weight we give to "some" in 3 [/b]
5. forkedknight
Defend the Universe
04 Jan '13 02:22
Originally posted by iamatiger
A. Some mathematics students have double majors. true if E is false, (because then all mathematics students are ed. majors, and we know some ed. majors have double majors) otherwise no evidence for this
There is no evidence for this being true, whether or not E is false. mathematics student != mathematics major.
6. talzamir
Art, not a Toil
04 Jan '13 22:00
A fun area of math, this.

education majors are, then, a subset of people who teach;
there is at least one edu major with a double major;
there is at least one math student who is an edu major.

A. Some mathematics students have double majors. false
B. Some of those with double majors student teach. false
C. All student teachers are education majors. false
D. All of those with double majors student teach. false
E. Not all mathematics students are education majors. false

So, in agreement with the previous posters. None of these necessarily follow.
7. 05 Jan '13 00:22
Originally posted by forkedknight
There is no evidence for this being true, whether or not E is false. mathematics student != mathematics major.
Ok, I will explain my reasoning:

1. All education majors student teach.
2. Some education majors have double majors.
3. Some mathematics students are education majors.

assuming E is false, E says: "Not all mathematics students are education majors."
So if it is false then All mathematics students are education majors.
We know from 1. that all education majors are student teachers, so we can conclude that all mathematics students are student teachers, then:

A. Some mathematics students have double majors.
I agree with forked knight, there is no guarantee that the education majors with double majors include any who were originally mathematics students, my bad .

B. Some of those with double majors student teach. definitely true because of 1 and 2, we know all education majors are student teachers, and some of them have double majors.

C. All student teachers are education majors. No evidence for this, one of the teachers could be a duck for all we can tell

D. All of those with double majors student teach. no evidence for this

E. Not all mathematics students are education majors. I would tend to be on the side of this being true, as the question setter seems to have deliberately used "some" in fact 3 about the mathematics majors, implying that not "all" of them are education majors
8. 05 Jan '13 00:251 edit
Its inaccurate to say any of these statements are definitely "false", the majority are "not proven" at worst.
9. talzamir
Art, not a Toil
05 Jan '13 13:271 edit
Still, given the wording.. "necessarily follows".. the answer would be, "none." All we know that there is at least one math major who is into education, at least one education student with a double major, and no education major who wouldn't teach. All else is maybes and perhapses.
10. 05 Jan '13 22:511 edit
Originally posted by talzamir
Still, given the wording.. "necessarily follows".. the answer would be, "none." All we know that there is at least one math major who is into education, at least one education student with a double major, and no education major who wouldn't teach. All else is maybes and perhapses.
Ah yes, you are right, none follow. The wording with education majors, double majors, education students etc. confused me!
11. joe shmo
Strange Egg
06 Jan '13 07:33
Originally posted by talzamir
Still, given the wording.. "necessarily follows".. the answer would be, "none." All we know that there is at least one math major who is into education, at least one education student with a double major, and no education major who wouldn't teach. All else is maybes and perhapses.
That's not what the author says.

She claims "B" follows
12. Agerg
The 'edit'or
08 Jan '13 01:152 edits
Originally posted by talzamir
Still, given the wording.. "necessarily follows".. the answer would be, "none." All we know that there is at least one math major who is into education, at least one education student with a double major, and no education major who wouldn't teach. All else is maybes and perhapses.
I might be missing something here but surely from "some education majors have double majors" we can conclude the set D of all people with double majors contains at least one person with an education major. Accordingly the set of all people with double majors contains at least one person who student teaches (by 1); which is the same as saying some of those who have double majors student teach.
As such I get that B follows from 1 and 2
13. forkedknight
Defend the Universe
08 Jan '13 04:40
Originally posted by Agerg
I might be missing something here but surely from "some education majors have double majors" we can conclude the set D of all people with double majors contains at least one person with an education major. Accordingly the set of all people with double majors contains at least one person who student teaches (by 1); which is the same as saying some of those who have double majors student teach.
As such I get that B follows from 1 and 2
Agreed
14. talzamir
Art, not a Toil
08 Jan '13 09:32
Rewording, keeping logically equivalent:
1. There are no education majors who don't teach.
2. There is at least one education major with a double major.
3. There is at least one math student who is an education major.

1,2: There is at least one education major with a double major, and that person, just like all edu majors, teaches.

So yes, agreed. B follows.

B. Some of those with double majors student teach.