Proof Writing for Dummies: Intersection & Union Elements

[woundedtiger4]

Problem: Prove that any element in the intersection of two sets is also in their union.

I am reading a proof writing book for dummies & the solution given in text is:

http://tinypic.com/r/141hn7/5

http://tinypic.com/r/141hn7/5


First Question:
In exam/test, is it OK if I write the Statements only or do I need to write reasons as well (as shown in the pic). As, we are not suppose to write the proof in form of table but with every statement (which is already logically very clear in the pic) do I need to write the reason as well?

Second Question:

http://tinypic.com/r/et70jq/5

http://tinypic.com/r/et70jq/5

Similarly, if it is easy to draw figures then is it compulsory to add like this?

PS. I will appreciate if your answers are in YES/NO form.

 

[micromass]

Oh God, two column proofs. There is no better way to make proofs look ugly...

Anyway:

In exam/test, is it OK if I write the Statements only or do I need to write reasons as well (as shown in the pic).

Statements only are ok. The reasons don't need to be given.

As, we are not suppose to write the proof in form of table but with every statement (which is already logically very clear in the pic) do I need to write the reason as well?

No. And I encourage you not to write proofs using those stupid tables.

Second Question:

http://tinypic.com/r/et70jq/5

http://tinypic.com/r/et70jq/5

Similarly, if it is easy to draw figures then is it compulsory to add like this?

No. It's not compulasory.

 

[Stephen Tashi]

In exam/test, is it OK if I write the Statements only or do I need to write reasons as well (as shown in the pic)..

There is no universal standard for writing proofs. How you write them depends on who you will read them. If the reader will be a teacher or grader, you must determine what they expect. If the reader is the editor of a math journal, you can look at past issues of the journal and see what style of writing proofs was accepted for publication. The style you see in math journals is very different from the style that teachers expect in elementary courses.

Like micromass, I'm not enthusiastic about the two column style of writing proofs. However, some teachers may expect this since it can make homework simpler to grade.

 

[woundedtiger4]

Oh God, two column proofs. There is no better way to make proofs look ugly...

Anyway:



Statements only are ok. The reasons don't need to be given.



No. And I encourage you not to write proofs using those stupid tables.



No. It's not compulasory.

Thanks a lot. God bless you. I am so much relieved :)