التمرين 3:
أكمل بأحد الرموز التالية:
\(\in, \notin, \subset, \not\subset\)
\(-3 \ldots \mathbb{Z}\)
\(\mathbb{N} \ldots \mathbb{N}\)
\(\frac{8}{2} \ldots \mathbb{Z}\)
\(-5 \ldots \mathbb{Z}\)
\(7 \ldots \mathbb{N}\)
\(\{-3,-2,-1,0,1,2,3\} \ldots \mathbb{Z}\)
\(\{-3,0,1,2\} \ldots \mathbb{Z}\)
\(\{0,1,2,-3\} \ldots \mathbb{Z}\)
\(\{0\} \ldots \mathbb{Z}\)
عرض التصحيح
-3 ∈ ℤ
ℕ ⊂ ℕ
8/2 ∈ ℤ
-5 ∈ ℤ
7 ∈ ℕ
{-3,-2,-1,0,1,2,3} ⊂ ℤ
{-3,0,1,2} ⊂ ℤ
{0,1,2,-3} ⊂ ℤ
{0} ⊂ ℤ
التمرين 4:
\(F = \{-5,-2,0,+4,+1,+7\}\) ,
\(E = \{-6,-5,+2,-3,4,0,-1,-4\}\)
\(0 \ldots E\)
\(2 \ldots E\)
\(-4 \ldots E\)
\(\begin{pmatrix}16 \\ 10\end{pmatrix} \ldots E\)
\(\{4,+7\} \ldots F\)
\(\{-1,+1\} \ldots F\)
\(F \cap \mathbb{N}\)
\(E \cup F\)
\(E \cap \mathbb{Z}\)
\(E \cap F\)
عرض التصحيح
0 ∈ E
2 ∉ E
-4 ∈ E
(16,10) ∉ E
{4,7} ⊂ F
{-1,1} ⊄ F
F ∩ ℕ = {0,1,4,7}
E ∪ F = {-6,-5,-4,-3,-2,-1,0,1,2,4,7}
E ∩ ℤ = E
E ∩ F = {-5,0}
التمرين 5:
\(A = \{0,1,2,-2,5,-5\}\) ,
\(B = \{0,-1,2,-5\}\) ,
\(C = \{0,2,5\}\)
\(0 \ldots \mathbb{Z}\)
\(C \ldots A\)
\(C \ldots \mathbb{N}\)
\(C \ldots B\)
\(\{0,-2,-5\} \ldots A\)
\(4 \ldots B\)
\(\{0\} \ldots \mathbb{Z}\)
\(\{0\} \ldots B\)
\(A \cap C\)
\(A \cap B\)
\(A \cap \mathbb{Z}\)
\(A \cap \mathbb{N}\)
\(B \cup C\)
\(A \cup C\)
\(A \cup B\)
\(B \cap C\)
عرض التصحيح
0 ∈ ℤ
C ⊂ A
C ⊂ ℕ
C ⊄ B
{0,-2,-5} ⊂ A
4 ∉ B
{0} ⊂ ℤ
{0} ⊂ B
A ∩ C = {0,2,5}
A ∩ B = {0,2,-5}
A ∩ ℤ = A
A ∩ ℕ = {0,1,2,5}
B ∪ C = {-5,-1,0,2,5}
A ∪ C = A
A ∪ B = A
B ∩ C = {0,2}
التمرين 6:
\(A = \{0,1,3,-9\}\) ,
\(B = \{0,-1,3,7,9,-9\}\) ,
\(C = \{0,3,7,-9\}\)
\(-1 \ldots \mathbb{N}\)
\(-8 \ldots \mathbb{N}\)
\(A \ldots B\)
\(\{-3,-9\} \ldots B\)
\(7 \ldots B\)
\(C \ldots \mathbb{N}\)
\(B \ldots \{0,3\}\)
\(\{-8\} \ldots \mathbb{Z}\)
\(C \ldots B\)
عرض التصحيح
-1 ∉ ℕ
-8 ∉ ℕ
A ⊄ B
{-3,-9} ⊄ B
7 ∈ B
C ⊄ ℕ
B ⊄ {0,3}
{-8} ⊂ ℤ
C ⊂ B