# Thread: find following sets help

1. ## find following sets help

Hey guys, need help with this one.

Let $\displaystyle \varepsilon = \mathbb{R}$, $\displaystyle A = \{ x \epsilon \mathbb{R} : x > 0 \}$ , $\displaystyle B = \{ x \epsilon \mathbb{R} : x > e \}$ , $\displaystyle C = \{ x \epsilon \mathbb{R} : x < \pi \}$ , where $\displaystyle e = 2.718$ and $\displaystyle \pi = 3.142$. Find the following sets:

a)
$\displaystyle A \cup B$

My Answer: $\displaystyle x > 0$

b) $\displaystyle B \cup C$

My Answer: $\displaystyle e < x < \pi$

c) $\displaystyle A \cap B$

My Answer: $\displaystyle x > e$

d) $\displaystyle B \cap C$

$\displaystyle e < x < \pi$

e) $\displaystyle \overline{A}$

My Answer: $\displaystyle x \leq 0$

f) $\displaystyle \overline{C}$

My Answer: $\displaystyle x \geq \pi$

g)
$\displaystyle A \backslash B$

h) $\displaystyle B \backslash C$

Any help and check on my answers would be much appreciated!

2. Hello!

I am afraid somethings wrong there

Originally Posted by jvignacio
Hey guys, need help with this one.

Let $\displaystyle \varepsilon = \mathbb{R}$, $\displaystyle A = \{ x \epsilon \mathbb{R} : x > 0 \}$ , $\displaystyle B = \{ x \epsilon \mathbb{R} : x > e \}$ , $\displaystyle C = \{ x \epsilon \mathbb{R} : x < \pi \}$ , where $\displaystyle e = 2.718$ and $\displaystyle \pi = 3.142$. Find the following sets:

a)
$\displaystyle A \cup B$

My Answer: $\displaystyle x > 0$
Yes!

Originally Posted by jvignacio

b) $\displaystyle B \cup C$

My Answer: $\displaystyle e < x < \pi$
No!
You should get suspiscious because of d).

It is ,

What does that mean? Well, it's like the intervall $\displaystyle (-\infty, \pi)$

x should be smaller than pi. Minus 50013 is smaller than pi, isn't it?

,

is similar to $\displaystyle x\in (e, + \infty)$

e < pi, so B u C = IR

Originally Posted by jvignacio
c) $\displaystyle A \cap B$

My Answer: $\displaystyle x > e$

d) $\displaystyle B \cap C$

$\displaystyle e < x < \pi$

e) $\displaystyle \overline{A}$

My Answer: $\displaystyle x \leq 0$

f) $\displaystyle \overline{C}$

My Answer: $\displaystyle x \geq \pi$
Yep, that's correct.

Originally Posted by jvignacio

g)
$\displaystyle A \backslash B$

$\displaystyle A = (0, \infty)$

because A is defined for all x > 0

The set B is defined for all x > e

so $\displaystyle B = (e, \infty)$

A without B = (0, e), e. g.

Edit: Ops, that would be $\displaystyle B = \{ x \in \mathbb{R} : 0 < x < e \}$ I'm sorry, I used the wrong definition of B

$\displaystyle A \backslash B = \{ x \in \mathbb{R} : 0 < x < e \}$

Originally Posted by jvignacio

h) $\displaystyle B \backslash C$

B = (0, e)

$\displaystyle C = (-\infty, pi)$

Note that pi > e, so $\displaystyle B \subset C$

That's why $\displaystyle B \backslash C = \emptyset$

3. Originally Posted by Rapha
Hello!

I am afraid somethings wrong there

No!
You should get suspiscious because of d).

It is ,

What does that mean? Well, it's like the intervall ($\displaystyle -\infty$, $\displaystyle \pi$)

x should be smaller than pi. Minus 50013 is smaller than pi, isn't it?

,

is similar to (e, $\displaystyle + \infty$)

e < pi, so B u C = IR
thanks for the reply! does IR mean all Real numbers?

4. Originally Posted by jvignacio
thanks for the reply! does IR mean all Real numbers?
You're welcome.

IR is supposed to mean the real numbers. I was kinda lazy using LaTeX, sorry for that

$\displaystyle (-\infty, 3.14) \cup (2.718, + \infty) = (-\infty, +\infty) = \mathbb{R}$

5. Originally Posted by Rapha
You're welcome.

IR is supposed to mean the real numbers. I was kinda lazy using LaTeX, sorry for that

$\displaystyle (-\infty, 3.14) \cup (2.718, + \infty) = (-\infty, +\infty) = \mathbb{R}$
ahh yeah thanks for that! Also is $\displaystyle A \backslash B$ the same as$\displaystyle A - B$ ? meaning A without B....

6. Originally Posted by Rapha

h) $\displaystyle B \backslash C$

$\displaystyle B = (0, e)$

C = ($\displaystyle -\infty$, $\displaystyle \pi$)

Note that $\displaystyle pi > e$, so $\displaystyle B \subset C$

That's why $\displaystyle B \backslash C = \emptyset$
Sorry isn't $\displaystyle B = (e, \infty)$ ? not $\displaystyle B = (0, e)$

So B without C = $\displaystyle x > \pi$ ?

7. Originally Posted by jvignacio
Sorry isn't $\displaystyle B = (e, \infty)$ ? not $\displaystyle B = (0, e)$

So B without C = $\displaystyle x > \pi$ ?

Arghhhh ****

You're right! $\displaystyle B = (0, \infty)$. So B without C = $\displaystyle x > \pi$ is correct

ahh yeah thanks for that! Also is the same as ? meaning A without B....
Probably not, what is the definition of A-B?

8. Originally Posted by Rapha
Arghhhh ****

You're right! $\displaystyle B = (0, \infty)$. So B without C = $\displaystyle x > \pi$ is correct

Probably not, what is the definition of A-B?

Ummm i thought it ment the same thing! If it doesn't Im not sure what the meaning of it is

9. Originally Posted by jvignacio

Ummm i thought it ment the same thing! If it doesn't Im not sure what the meaning of it is
...Could be.

It depends on the definition you use.

If $\displaystyle A\backslash B = \{ x \in A : x \notin B \} := A - B$ then they are the same, but I know the definition

$\displaystyle A - B = \{ x - y : x \in A, y \in B \}$

as well. That would be something different.

10. Originally Posted by Rapha
...Could be.

It depends on the definition you use.

If $\displaystyle A\backslash B = \{ x \in A : x \notin B \} := A - B$ then they are the same, but I know the definition

$\displaystyle A - B = \{ x - y : x \in A, y \in B \}$

as well. That would be something different.
Ill get back to you thanks for the help mate!