1 szkoły ponadpodstawowej

I liceum

I technikum

Matematyka 1. Zakres podstawowy

A={1,2,5,10} B={0,1,9,13,64,121} &nbsp; C={5,−2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​,0,−1,−π} &nbsp; D={−1,−2,53​,77<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​​,413​} &nbsp;&nbsp;

A={x: x=3n i n∈N} &nbsp; B={x: x2=16} &nbsp; C={x: x=5n1​ i n∈N+​} &nbsp; D={x: x3−5&gt;22} &nbsp; E={7x: x∈N} &nbsp; F={x: x1​≥2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​} &nbsp; G={x: x+x2≤4} &nbsp;

Zbiór&nbsp; A &nbsp;jest podzbiorem zbioru&nbsp; B ( &nbsp;co oznaczamy&nbsp; A⊂B) &nbsp;wtedy, gdy każdy element zbioru&nbsp; A &nbsp; jest elementem zbioru&nbsp; B. &nbsp; Pamiętajmy też, że podzbiorem każdego zbioru&nbsp; A &nbsp;jest ten sam zbiór&nbsp; A (A⊂A) &nbsp; i podzbiorem każdego zbioru&nbsp; A &nbsp;jest zbiór pusty&nbsp; (∅⊂A). &nbsp; <hr> a) &nbsp;&nbsp;Podzbiory zbioru&nbsp; A: {a}, ∅. b) &nbsp;&nbsp;Podzbiory zbioru&nbsp; B: {a}, {b}, {a, b}, ∅. &nbsp; c) &nbsp;Podzbiory zbioru&nbsp; C: {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, ∅. &nbsp;

Sumą zbiorów&nbsp; A &nbsp;oraz&nbsp; B ( ozn.&nbsp; A∪B) &nbsp;nazywamy zbiór tych elementów,
które należą do zbioru&nbsp; A &nbsp;lub do zbioru&nbsp; B. &nbsp;
Część wspólną zbiorów (iloczyn zbiorów)&nbsp; A &nbsp;oraz&nbsp; B ( ozn.&nbsp; A∩B) &nbsp;nazywamy zbiór tych elementów,
które należą jednocześnie do zbioru&nbsp; A &nbsp;i do zbioru&nbsp; B. &nbsp; &nbsp; &nbsp; 
<hr>
a)
A∪B={1,2,3,4,5,6,7,8} &nbsp;
A∩B={3,5}
<hr>
b)
A∪B={1,2,3,4,5} &nbsp;
A∩B={4,5} &nbsp;
<hr>
c)
A∪B={0,3,6,9,12,15,18,21,24,27,30} &nbsp;&nbsp;
A∩B={0,6,12,18,24,30} &nbsp;
<hr>
d)
A∪B={1,2,3,4,5,6,…,19,20} &nbsp;
A∩B=∅ &nbsp;

Komentarze