في هذا الدرس نتعرف على العلاقات الثنائية او ما يسمي بقوانين التركيب الداخلية. نقدم التعاريف الضرورية ثم نحل مجموعة من التنارين المتنوعة We present several examples of binary realtions. We will also solve many questions related to this defintion

1. Abstract Algebra : binary realtions solved
problems
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2. Abstract Algebra
Binary Relation
E = ∅
f : E × E → E
E
b a f (a, b) E b a
a⊥b a ∧ b aTb a ∗ b
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3. Abstract Algebra
f : N × N → N
(a, b) → a − b
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4. Abstract Algebra
f : Q × Q → Q
(a, b) → |a| − |b|
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5. Abstract Algebra
T
f : T × T → T
(C1, C2) → C
C2 C1 C
f
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6. Abstract Algebra
P P
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7. Abstract Algebra
P P
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8. Abstract Algebra
(C(a, b), R, <)
R (a, b)
(C(a, b), R, <)
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9. Abstract Algebra
E = {n2, n ∈ N}
(N, +) E
(N, ×) E
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10. Abstract Algebra
N N2 N1
E = {2k + 1k ∈ N}
(N2, +) (N1, +) E
(N2, ×) (N1, ×) E
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11. Abstract Algebra
N N2 N1
f : N1 × N1 → N1
(a, b) → a + b
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12. Abstract Algebra
N N2 N1
f : N2 × N2 → N2
(a, b) → a × b
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13. Abstract Algebra
∆ E P(E)
A∆B = (A − B) ∪ (B − A)
φ : P(E) × P(E) → P(E)
(A, B) → A∆B
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14. Abstract Algebra
α E P(E)
AαB = (A − B)
ψ : P(E) × P(E) → P(E)
(A, B) → AαB
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15. Abstract Algebra
α E P(E)
AαB = (A − B)
ψ : P(E) × P(E) → P(E)
(A, B) → AαB
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16. Abstract Algebra
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