# Sets + Union ??

#### BluebellDementia

##### New member
Good evening/morning/night (or whatever time of the day it is for you)

(I hope this is in the right section, I apologize if it isn't)
I would like to jump straight to the point, I am a first year college student and I have my Math preliminary exam in about... Four or so hours and there's been something that I don't quite understand how to answer from notes I have, (I was absent that day regarding this question in particular and was stupid enough not to ask the professor about it sooner)

Here is the question, copy pasted:
_____________

3. In each of the following, determine which one of the sets N, J, Q H, R and Ø is equal to the given set.
a) J U Q

b) J (intersection) Q

c) N (intersection) H

d) H U R
______________

Does anyone know how to answer this question? We had previous ones that I knew how to answer (which I will post below) and I understand what this question asks, I just don't know how to answer it. For example, in the first question I know it says: The integer set Union the Rational set = (and then you add one of the above listed sets I guess?) I'm not quite sure what they mean. Any help would be greatly appreciated <3

Here are some of the previous questions (That I knew how to answer):

1. Insert or in the blank to make the statement correct.

a) 15____ N e) 0____ Q
b) 1.41421____H f) 2009____ J
c) -3____ J g) ____ R
d) ____ Q h) -5____ H.

2. Insert or in the blank to make the statement correct.

a) N ____ Q
b) R ____ Q
c) J ____ N
d) J ____ R
e) R ¬____ N
f) J ____ Q
g) H ____ R
h) {0} ____ J

#### lookagain

##### Senior Member
BluebellDementia said:
Here is the question, copy pasted:
_____________

3. In each of the following, determine which one of the sets N, J, Q H, R and Ø is equal to the given set.
a) J U Q

b) J (intersection) Q

c) N (intersection) H

d) H U R
______________
What sets (what types) of numbers are meant by the sets N, J, Q, H, and R, respectively?

#### BluebellDementia

##### New member
lookagain said:
BluebellDementia said:
Here is the question, copy pasted:
_____________

3. In each of the following, determine which one of the sets N, J, Q H, R and Ø is equal to the given set.
a) J U Q

b) J (intersection) Q

c) N (intersection) H

d) H U R
______________
What sets (what types) of numbers are meant by the sets N, J, Q, H, and R, respectively?
(Thanks for replying on such short notice)

N = Natural numbers
J = Integers
Q = Rational numbers
H = Irrational numbers
R = Real numbers

#### lookagain

##### Senior Member
BluebellDementia said:
lookagain said:
BluebellDementia said:
3. In each of the following, determine which one of the sets N, J, Q H, R and Ø is equal to the given set.
a) J U Q

b) J (intersection) Q

c) N (intersection) H

d) H U R
______________
N = Natural numbers
J = Integers
Q = Rational numbers
H = Irrational numbers
R = Real numbers
a) The set of integers in union with the set of rational numbers gives the set of rational numbers,
because the set of integers is a subset of the set of rational numbers. $$\displaystyle **$$ $$\displaystyle \boxed{ Q}$$

b) The intersection of the set of integers with the set of rational numbers is the set of integers,
because the intersection is more restrictive. See $$\displaystyle **$$ above. $$\displaystyle \boxed{ J}$$

c) The intersection of the set of natural numbers with the set of irrational numbers is the empty set, or $$\displaystyle \{\ \}\$$,
because the set of natural numbers is a subset of the set of rational numbers. But the set of rational numbers
and the set of irrational numbers have no elements in common. $$\displaystyle \boxed{ \{\ \} }$$

d) The union of the set of irrational numbers with the set of real numbers is the set of real numbers,
because the set of irrational numbers is a subset of the set of real numbers. $$\displaystyle \boxed{ R}$$

#### BluebellDementia

##### New member
Thank you so much for your help, sorry I was so late in thanking you!