B - Prírodovedecká fakulta - Univerzita Komenského
B - Prírodovedecká fakulta - Univerzita Komenského
B - Prírodovedecká fakulta - Univerzita Komenského
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Učebné texty z matematiky pre 1. ročník geológie<br />
12<br />
Riešenie.<br />
a. A ∩ B = { 1 , 2}<br />
= B , A ∪ B = { , 2,<br />
3}<br />
= A<br />
1 , − B = { 3}<br />
A , B − A = { }<br />
b. A ∩ B = {} , A ∪ B = { orech,<br />
jablko,<br />
hruška,<br />
koleso}<br />
, A − B = { orech,<br />
jablko}<br />
= A ,<br />
{ hruška koleso}<br />
B<br />
B − A = , =<br />
5<br />
6<br />
A ∩ i , A ∪ B = { x } B<br />
i=<br />
1 i = i=<br />
c. B = { x } = A<br />
, − B = { }<br />
1<br />
−<br />
− B = Z 0<br />
A , B − A = { x }<br />
d. A ∩ B = ℵ = B , A ∪ B = Z = A,<br />
A , B − A = { }<br />
Príklad 4. Zisti A ∩ B ∩ C ∩ D a A ∪ B ∪ C ∪ D .<br />
a. A={1};<br />
D={1,2,3,4}<br />
B={1,2}; C={1,2,3};<br />
b. A={1};<br />
D={2,3,4,5}<br />
B={1,2}; C={1,2,3};<br />
Riešenie.<br />
a. A ∩ B ∩ C ∩ D = 1,<br />
A ∪ B ∪ C ∪ D = { 1,<br />
2,<br />
3,<br />
4}<br />
b. ∩ B ∩ C ∩ D = { }<br />
A , A ∪ B ∪ C ∪ D = { 1,<br />
2,<br />
3,<br />
4,<br />
5}<br />
c. A ∩ B ∩ C ∩ D = ℵ,<br />
A ∪ B ∪ C ∪ D = ℜ<br />
d. ∩ B ∩ C ∩ D = { }<br />
A , A ∪ B ∪ C ∪ D = ℜ<br />
e. ∩ B ∩ C ∩ D = { }<br />
A , A ∪ B ∪ C ∪ D = ℜ<br />
c. A=Z, B=ℵ, C=Q, D=ℜ<br />
d. A=Z, B=ℵ, C=ℜ , D={0}<br />
e. A=Z, B=ℵ , C=ℜ , D={}<br />
Príklad 5. V ktorých prípadoch ( A B)<br />
∪ C = A ∩ ( B ∪ C)<br />
a. A={1}; B={1,2}; C={1,2,3}<br />
b. A={♥}; B={♣♦♠}; C={♣♠}<br />
Riešenie.<br />
a. ( A ∩ B)<br />
∪ C = { 1 , 2,<br />
3}<br />
≠ A ∩ ( B ∪ C)<br />
= { 1}<br />
b. ( A ∩ B)<br />
∪ C = C ≠ A ∩ ( B ∪ C)<br />
= { }<br />
∩ ?<br />
6<br />
c. A={ } 5<br />
x i ; B={ } i=<br />
1<br />
6<br />
x i ; C={ } i=<br />
1<br />
7<br />
x i i=<br />
1<br />
d. A=Z; B=ℜ ; C={}<br />
c. ( A ∩ B)<br />
∪ C = C ≠ A ∩ ( B ∪ C)<br />
= A<br />
d. ( A ∩<br />
B)<br />
∪ C = Z = A ∩ ( B ∪ C)