Zadania  przedziały liczbowe, działania na zbiorach
Zad. 1. Dla danych zbiorów A, B zaznacz na osi A *" B, A )" B, A - B, B - A oraz zapisz wynik
w postaci przedziału lub sumy przedziałów:
n) A = (- 5; 4), B = (- 4; 0)
a) A = (- 8;1 , B = (- 3; 4
o) A = -1; 3 , B = 0; 1
b) A = - 2; 8), B = 5; 10)
p) A = (- 4; 1 , B = - 2; 0)
c) A = (- 4; - 2), B = (- 3; 0)
d) A = - 9; - 5 , B = - 5; -1 q) A = - 5;1), B = (- 3; 0
e) A = (- 3; 0 , B = 0; 5) r) A = (-10; -1 , B = (1; 10
f) A = 0; 5), B = (2;13 s) A = - 7; - 3), B = -1; 3)
t) A = (- 4; 0), B = (4;10)
g) A = (- "; -10 , B = (- "; 10
u) A = - 2; -1 , B = 0; 2
h) A = - 3; + "), B = -1; + ")
v) A = (- 8; - 2 , B = 0; 8)
i) A = (- "; - 8 , B = - 5; + ")
w) A = - 5; 0), B = (0; 5
j) A = (- "; - 2 , B = - 2; + ")
x) A = (- "; + "), B = (5; + ")
k) A = (- "; 9 , B = -12; + ")
y) A = (- "; + "), B = (- "; 7
l) A = (1;7*#, B = (3;5*#
m) A = )#0; 1), B = )#-1; 2) z) A = (- "; + "), B = 3; 8
Zad. 2. Zapisz zbiór A w postaci przedziału lub sumy przedziałów, zaznacz zbiór A na osi
liczbowej:
a) A = {x " R : x > -2 lub x d" 2} g) A = {x " R : x e" 3 lub x < -1}
b) A = {x " R : x > -5 lub x e" -4} h) A = {x " R : x < 3 lub x d" -4}
c) A = {x " R : x d" 0 lub x e" 2} i) A = {x " R : x < -3 lub x > -5}
d) A = {x " R : x e" -1 i x < 0} j) A = {x " R : x > -2 i x d" 0}
e) A = {x " R : x e" -1 i x e" 1} k) A = {x " R : x > 2 i x d" -2}
f) A = {x " R : x < 0 i x > 1} l) A = {x " R : x d" 1 i x < -2}
Zad. 3. Rozwią\
równanie. Zad. 4. Rozwią\
nierówność.
a) 2x = 3 a) - x - 5 > -3x - 7
b) 3x + 1 = 0
b) - x + 3 d" 3x - 4
c) -4x + 2 = 3
c) x(x + 2) < x2 + 3x + 1
d) x + 4 = 2x  5
d) 2x + 3 > 2(x+1)
e) -2x + 4 - x = -3x  5
e) 3x + 1 > 3(x +1) +1
f) 5x + 3  2x - 1 = 2x  5 + x + 7
f) - x - 5 - 2x d" 2 - 3x - 7
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Zadania  przedziały liczbowe, działania na zbiorach
Odpowiedzi:
Zad. 1.
a) A *" B = (- 8; 4 , A )" B = (- 3; 1 , A - B = (- 8; - 3 , B - A = (1; 4
b) A *" B = - 2, 10), A )" B = 5, 8), A - B = - 2, 5), B - A = 8, 10)
c) A *" B = (- 4, 0), A )" B = (- 3, - 2), A - B = (- 4, - 3 , B - A = - 2, 0)
d) A *" B = - 9; -1 , A )" B = - 5; - 5 = {5}, A - B = - 9; - 5), B - A = (- 5, -1
e) A *" B = (- 3; 5), A )" B = 0; 0 = {0}, A - B = (- 3; 0), B - A = (0, 5)
f) A *" B = 0; 13 , A )" B = (2; 5), A - B = 0; 2 , B - A = 5; 13
g) A *" B = (- "; 10 , A )" B = (- "; -10 , A - B = ", B - A = (-10; 10*#
h) A *" B = )#-3; + "), A )" B = )#-1; + "), A - B = )#-3; -1), B - A = "
i) A *" B = (-"; - 8*# *" )#-5; + "), A )" B = ", A - B = (-"; - 8*#, B - A = )#-5; + ")
j) A *" B = (-"; + "), A )" B = {- 2}, A - B = (-"; - 2), B - A = (2; + ")
k) A *" B = (-"; + "), A )" B = )#-12; 9*#, A - B = (-"; -12), B - A = (-9; + ")
l) A *" B = (1; 7*#, A )" B = (3; 5*#, A - B = (1; 3*# *" (5; 7*#, B - A = "
m) A *" B = )#-1; 2), A )" B = )#0; 1), A - B = ", B - A = )#-1; 0) *" )#1; 2)
n) A *" B = (-5; 4), A )" B = (-4; 0), A - B = (-5; - 4*# *" )#0; 4), B - A = "
o) A *" B = )#-1; 3*#, A )" B = )#0; 1*#, A - B = )#-1; 0) *" (1; 3*#, B - A = "
p) A *" B = (-4; 1*#, A )" B = )#-2; 0), A - B = (-4; - 2*# *" )#0; 1*#, B - A = "
q) A *" B = )#-5; 1), A )" B = (-3; 0*#, A - B = )#-5; - 3*# *" (0; 1), B - A = "
r) A *" B = (-10; -1*# *" (1; 10*#, A )" B = ", A - B = (-10; -1*#, B - A = (1; 10*#
s) A *" B = )#-7; - 3) *" )#-1; 3), A )" B = ", A - B = )#-7; - 3), B - A = )#-1; 3)
t) A *" B = (-4; 0) *" (4; 10), A )" B = ", A - B = (-4; 0), B - A = (4; 10)
u) A *" B = )#-2; -1*# *" )#0; 2*#, A )" B = ", A - B = )#-2; -1*#, B - A = )#0; 2*#
v) A *" B = (-8; - 2*# *" )#0; 8), A )" B = ", A - B = (-8; - 2*#, B - A = )#0; 8)
w) A *" B = )#-5; 0) *" (0; 5*#, A )" B = ", A - B = )#-5; 0), B - A = (0; 5*#
x) A *" B = (- "; + "), A )" B = (5; + "), A - B = (- "; 5 , B - A = "
y) A *" B = (- "; + "), A )" B = (- "; 7 , A - B = (7; + " , B - A = "
z) A *" B = (- "; + "), A )" B = 3; 8 , A - B = (- "; 3)*" (8; + "), B - A = "
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Zadania  przedziały liczbowe, działania na zbiorach
Zad. 2.
a) A = (-"; + ") , b) A = (-5 ;+") , c) A = (-"; 0*# *" )#2; + ") , d) A = )#-1 ;0) , e) A = 1; + ") ,
f) A = " , g) A = (-"; -1)*" )#3; + ") , h) A = (-"; 3), i) A = (-"; + ") , j) A = (-2; 0*# , k) A = " ,
l) A = (-"; - 2).
Zad. 3.
1 1
a) x = 1,5, b) x = - , c) x = - , d) x = 9, e) x " " , f) x " R .
3 4
Zad. 4.
a) x "(-1; + "), b) x " 1,75; + " ), c) x "(-1; + "), d) x " R , e) x " " , f) x " R .
3