1 szkoły ponadpodstawowej

I liceum

I technikum

Matematyka poznać, zrozumieć 1. Zakres podstawowy. Po gimnazjum

a) Zaznaczmy oba zbiory na osi liczbowej

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/33269/YdLEAovVMFOzEvbaALCB0A%3D%3D_2f121fe2512e078fe09b0d3a27817aed557269d577e99e99762acf8e304683c6.png">
Spójrzmy na rysunek, na którym zaznaczono przedział A oraz iloczyn przedziałów A i B,&nbsp; i ustalmy, co możemy z niego wywnioskować o przedziale B:

<ul>
<li>do przedziału B nie należy liczba -4, gdyż nie należy ona do części wspólnej </li>
</ul>

a) &nbsp; <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/33286/szcDpsiPmVLSo8w%2Bh2vviw%3D%3D_019e48f28aa536425874c8a38083e6ee7b599b1ef73437e9354c409937da7904.png"> A∪B=(−5,6) A∩B=(−3,4) A\B=(−5,−3⟩ B\A=⟨4,6)

a) &nbsp; <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/33293/CNfRESa/uWqICEl2nQy3Zg%3D%3D_300db9c54845f0f9e98ce04bfb46029ad9871cdbaa4f51a7a9c94c09d3a9dd0f.jpg" width="744" height="186"> &nbsp; (−∞,−5⟩∪⟨4,+∞)

a) 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>​≈1,42 N∩(−∞,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>​)={0,1,2,3,4,5,…}∩(−∞,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}

Podane przedziały odczytujemy z poniższego rysunku, na który naniesiono przedziały A,B,C,D. <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/33297/4eRNilqdKs7Mwl71KYUAvg%3D%3D_8ff7993d8bdb42b21ebee3cdc9739b213188f24e72a44a78c2cd7b332640eeb1.jpg"> a) C∩D

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