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Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.

Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.

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Part 07 – Discrete Mathematics for GATE: Examples on Symmetry, Anti-Symmetry, and Asymmetry

1. Symmetric Relation (सममित संबंध)

यदि (a,b)∈R(a, b) \in R है, तो (b,a)∈R(b, a) \in R भी होना चाहिए।

Example 1: “Friendship Relation”

Example 2: “Equality Relation ( = )”

2. Anti-Symmetric Relation (प्रतिसममित संबंध)

यदि (a,b)∈R(a, b) \in R और (b,a)∈R(b, a) \in R दोनों सत्य हैं, तो a = b होना चाहिए।

Example 1: “Subset Relation (⊆)”

Example 2: “Divisibility Relation (|)”

3. Asymmetric Relation (असमान्य संबंध)

यदि (a,b)∈R(a, b) \in R है, तो (b,a)∉R(b, a) \notin R होना चाहिए।

Example 1: “Less Than Relation (<)”

Example 2: “Precedence Relation in Scheduling”

संबंधों की तुलना (Comparison Table)

Relation Type Definition Example
Symmetric यदि (a, b) ∈ R तो (b, a) भी ∈ R दोस्ती (Friendship), समानता (Equality)
Anti-Symmetric यदि (a, b) ∈ R और (b, a) ∈ R, तो a = b सबसेट (⊆), विभाज्यता (
Asymmetric यदि (a, b) ∈ R तो (b, a) ∉ R छोटा-बड़ा (<), प्राथमिकता (Precedence)

निष्कर्ष

GATE परीक्षा के लिए क्या आपको और अधिक प्रश्नों और हल की जरूरत है?

Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.

B.A.(Prog) Mathematics Discipline Specific Course (DSC-1)

Discrete Mathematical Structures