x
∈R x⊆R
x
xR
x/R
∈
{x ∈ R|x ≤ 1} {x ∈ Z| − 5 ≤ x ≤ 1000} {x ∈ N|5 ≤ x} {x ∈ Q|x ≤ 1} {4, 8, 6, 2} {9, 3, 7, 1, 5} 10 10 10 10
{∅} ∅ {vocales} {consonantes} {2, 4, 6, 8, 10}
5} {x ∈ N|x 5} {x ∈ N|x {x ∈ Z|x ≤ 5} {x ∈ Z|x ≥ 5} {2, 4, 6, 8, 10,...}
0 4 13 10
19 10 21 6
{x ∈ N : 0 < x ≤ 10} {0, 5, 10} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {5, 10} {0, 10} {0, 5, 10} √ 5
x = 20
x = 20
x≯6
x = 20
x > 6
x = 20
x≯6
x = 20
x≯6
x
1/3
√ 16 √ 2 10/2 100
×5 50 × 2 25 × 4 2 ×5 20
2
2
5 2/5 0/4 1/8 1,25 0,125
x > 6
8,1 1,8
P
∪Q P ∪ Q P ∩ Q P ∩ Q
x x > 4
⇒ x
x x≯4 x
⇒ x
⇒ x > 4
∈N
⇒x≯4 ⇒ x < 4 x
{0, 10}
x
≤ 10
x
x
∈N
{1, 3, 5, 7, 9} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} {2, 4, 6, 8, 10} x
{2, 3, 5, 7, 9} {5, 7, 9} {4, 6, 8, 10} {3, 5, 7} N⊆Z⊇Q⊆R N⊆Z⊆Q⊆R N⊇Z⊇Q⊇R N⊆Q⊆Z⊆R
P
∩ Q ∩ R P ∪ Q ∩ R P ∩ Q ∪ R P ∩ Q ∩ R
2 p + g
− 3r − (g − 3r + 2 p)
4 p + 2g
− 6r 4 p + 6r − 2g
p + g + r 0
x2 + 5x
− 24 = 0
2
x
− 8)(x + 3) (x + 8)(x − 3) (x − 8)(x − 3) (x
(x + 8)(x + 3)
∪ Q) ∩ R
(P
(6m3 2
2
2
2
4
3
2
2 2
4
(4m2 n4 )3 126 n7 64m5 n7 64m6 n7 64m6 n1 2 (2a2 + 4b2 )3 6a6 + 48a4 b2 + 96a2 b4 + 12b6 8a6 + 48a4 b2 + 96a2 b4 + 64b6 8a6
4 2
− 48a b
+ 96a2 b4
− 64b
6
8a6 + 48a2 + 96a4 b2 + 64b6
(2−1)÷x 5x÷4
− 8x −
10x
5 4 4
5x2
2
− 8m n + 20mn ) ÷ −2m
2
−3m + 4mn − 10n 3m − 4mn + 10n 3m + 4m − 10m n 12m + 4mn − 10mn
5/4 4 5x2
1
− 5(a + b) = (1/3)(a/b)
(1/5)(a + b) = 3(a/b) (1/5)a + b = 3(a/b) a + b/5 = (3a/3b)
− −
4 2
x
2
x
4
2
x
2
2x2 4x2
5 + 6x
− 3x
− 3x
3
p(x) = 5 + 2x
2
q (x) = 2 + 4x
2
−x
3
1 + 2x + 2x2 4x2
7x2
p(x) = 3 +2x + x2
3
− 3x
q (x) = 5x2
− 2x
− 3x + 2
− 5x + 3 2
−7x + 5x + 3 7x − 5x − 3 3x − x3 2
2
p(x) = 2x3 2x2 +3x+1
−
4
−2x
+ x2
− 4x + 1
2x4 + x2 + 4x + 1
2x4 0
2
−x
+ 4x
−1 p(x) = x4
2
q (x) = x + 1
3
− 2x
+ 3x2
− 2x + 2
q (x) = x+1
x2 x2
− 2x + 2 + 2x − 2 2
−x
+ 2x + 2 x 3
