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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(52879)   (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'
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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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