Day 02 – Discrete mathematics for gate in Hindi – Symmeteric Relation and it’s application.

Day 02 – Discrete mathematics for gate in Hindi – Symmeteric Relation and it’s application.

Here’s a detailed explanation of Symmetric Relation and its application, tailored for Day 02 of Discrete Mathematics for GATE (CSE/IT), explained in Hindi-English (Hinglish) for better understanding.

Day 02 – Discrete Mathematics for GATE

Topic: Symmetric Relation (साम्य संबंध)

1. Symmetric Relation क्या होता है?

Definition (परिभाषा):

एक relation R को Symmetric कहा जाता है अगर:

$$\text{For all }a,b\in A,\text{ अगर }(a,b)\in R\Rightarrow (b,a)\in R\text{ भी हो}$$

मतलब: अगर A ने B को प्यार किया, तो B ने भी A को प्यार किया — ये एक symmetric relation है

2. आसान उदाहरण:

Example 1:

Let A = {1, 2, 3}
Let R = {(1, 1), (2, 2), (1, 2), (2, 1)}

यहाँ (1, 2) है तो (2, 1) भी है ⇒ Symmetric Relation

Example 2:

R = {(1, 2), (2, 3)}

यहाँ (2, 1) और (3, 2) missing हैं ⇒ Not symmetric

3. Daily Life Example of Symmetric Relation:

Relation	Symmetric?	Why?
“is sibling of” (भाई/बहन है)	Yes	A भाई है B का, तो B भी A का भाई
“is father of” (पिता है)	No	A पिता है B का, B A का नहीं
“has same birthday as”	Yes	A का birthday B के जैसा है ⇒ B का भी A जैसा

4. Representation (Matrix form में):

Let R be a relation on set A = {1, 2}

If:

$$R=\{(1,2),(2,1)\}$$

Then matrix form:

Matrix is symmetric along diagonal ⇒ R is symmetric

5. GATE में Use और Application:

• Graph Theory:

  • Undirected graph ⇒ adjacency relation is symmetric

  • If A is connected to B, then B is also connected to A

• Relational Databases:

  • If record A relates to B in symmetric way, reverse must also exist

• Computer Networks:

  • Mutual connectivity, like peer-to-peer connections

6. GATE Practice Questions:

Q1. Which of the following relations are symmetric?

A = {1, 2, 3}
R1 = {(1,2), (2,1), (3,3)}
Ans: Symmetric

Q2. Which property is violated if (a,b) ∈ R but (b,a) ∉ R?

Ans: Symmetric Property

Summary Chart:

Bonus Tip for GATE:

• In relation-type MCQs, always test reflexive, symmetric, transitive properties individually.

• Matrix-based questions on symmetric relation are common in GATE.

Would you like a PDF version, video lecture link in Hindi, or a worksheet for practice on Symmetric Relations?

Day 02 – Discrete mathematics for gate in Hindi – Symmeteric Relation and it’s application.

Discrete Mathematics for Computer Science

Discrete Structures