SOLUTION: Let N = set of natural numbers; Z = set of integers; Q = set of rational numbers; Q' = set of irrational numbers; and R = set of real numbers Find the following sets: (

Question 1091471: Let N = set of natural numbers;
Z = set of integers;
Q = set of rational numbers;
Q' = set of irrational numbers; and
R = set of real numbers
Find the following sets:
(Z ∩ Q) U N =
(Q U Q') ∩ R =
(N U Z) U (Q ∩ R) =
(Q U R) ∩ N =
(Q U N)' ∩ R =
Q' ∩ Z =

*the options for the answers are: null set {}, Q, Z, N, R, and Q', but I can't get why. For example, for the first item, I tried finding what Z and Q had in common before having it in union with N, but I'm used to having this done with actual sets with elements... hence, I honestly don't know how to answer this.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Let N = set of natural numbers;
Z = set of integers;
Q = set of rational numbers;
Q' = set of irrational numbers; and
R = set of real numbers
Find the following sets:

(Z ∩ Q) U N =            a)   (Z ∩ Q) = Z (it is obvious and even more than obvious);
                         b)  Therefore,  (Z ∩ Q) U N = Z U N = Z  (again, it is obvious and even more than obvious).


(Q U Q') ∩ R =           a)  (Q U Q') = R (it is obvious);
                         b)  Therefore,  (Q U Q') ∩ R = R ∩ R = R  (it is obvious).


(N U Z) U (Q ∩ R) =      a)  (N U Z) = Z;  (Q ∩ R) = Q  (obvious)
                         b)  Therefore,  (N U Z) U (Q ∩ R) = Z U Q = Q.


(Q U R) ∩ N =


(Q U N)' ∩ R =


Q' ∩ Z =


*the options for the answers are: null set {}, Q, Z, N, R, and Q'

---------------
And so on . . . From this point, go ahead on your own.

I don't want to do ALL this simple work instead of you.

It is REALLY very SIMPLE.

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