Discrete Math help

[itrymath]

Hey guys, I'm new to the forum. Anyways long story short, I'm jean and I need some help from you smart gentlemen and ladies.

This is some HW that I am having trouble with, its for a Computer Science Theory course (more math than computer science theory so far).

So this course is built on top of Discrete Math, and I haven't taken that since Fall 2013 :\ and I'm still a little rusty on those things, professor is "Reviewing".

Basically I need help with these problems, just verify for me if its correct or not please and thank you. (My answers are in green.) And if its not correct, what did I do wrong?

1. Let A = { z ∈ R | 0 < z < 1} and B = { z ∈ R | 0 ≤ z ≤ 1}. Say whether each of the following statements is true or false
(a) ∀x ∈ A ( ∃y ∈ A (x > y) ). . .True
(b) ∀x ∈ A ( ∃y ∈ A (x ≥ y) ). . .False
(c) ∃y ∈ A ( ∀x ∈ A (x > y) ). . .True
(d) ∃y ∈ A ( ∀x ∈ A (x ≥ y) ). . .True
(e) ∀x ∈ B ( ∃y ∈ B (x > y) ). . .True
(f) ∀x ∈ B ( ∃y ∈ B (x ≥ y) ). . .True
(g) ∃y ∈ B ( ∀x ∈ B (x > y) ). . .False
(h) ∃y ∈ B ( ∀x ∈ B (x ≥ y) ). . . True

2. Give a recursive definition for {{{ ... }}}. Hint: such a definition should not need ellipses. Basically you need to formulate the set as V = { ... V ... V ... }, somehow, i.e. define V by using V in the definition itself.

I've got no idea how to define this :\ any hints?

3. Give a recursive definition for {1, {1, { ... }}}. Hint: such a definition should not need ellipses. Basically you need to formulate the set as W = { ... W ... W ... }, somehow, i.e. define W by using W in the definition itself.

{W | W is a set and S∈S}

So yeah... Any help is greatly appreciated. Any books to read that can quickly summarize Discrete Math would be GREATLY appreciated too.

 

[stapel]

1. Let A = { z ∈ R | 0 < z < 1} and B = { z ∈ R | 0 ≤ z ≤ 1}. Say whether each of the following statements is true or false
(a) ∀x ∈ A ( ∃y ∈ A (x > y) ). . .True

Can you prove this to be true? Or do you just "think" that this is true?

(b) ∀x ∈ A ( ∃y ∈ A (x ≥ y) ). . .False

Can you give a counter-example which proves this to be false? Or do you just "think" that this is false?

(I'm not saying that you're wrong -- or that you're right. I'm asking if you can prove your case.)

2. Give a recursive definition for {{{ ... }}}....

I've got no idea how to define this :\ any hints?

3. Give a recursive definition for {1, {1, { ... }}}....

{W | W is a set and S∈S}

Isn't (3) just a special case of (2)?