logic

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?

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.

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

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]

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.

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.

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

Its inaccurate to say any of these statements are definitely "false", the majority are "not proven" at worst.

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.

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!

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

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

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

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.