Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 10 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 10 Maths Textbook Solution.

Answers (1)

Answer: R is an equivalence relation. 
The set of all elements in A related to triangle T is the set of all triangles.
Hint: To prove equivalence relation it is necessary that the given relation should be reflexive, symmetric and transitive.
Given: \! R= \left \{ \left ( P_{1}, P_{2}\right ):P_{1}\, and\, P_{2} \: have\: same\: number\: o\! f\: sides \right \}
Explanation:
Reflexive:
R\: is\: re\! f\! lexive\: \text{ since } (P_{1}, P_{1})\epsilon \: R \: \text{ is }\: the\: same \: polygon\: as\: itsel\! f.
Symmetric:
Let (P_{1}, P_{2}) \epsilon \: R
P_{1}\, \text{ and }\, P_{2}\: have \: the \: same\: numbers\: o\! f\: sides.
P_{2}\, \text{ and }\, P_{1} \: \text{ have }\: the\: same \: number \: o\! f \: side.
(P_{2}, P_{1}) \epsilon \: R
R is symmetric
Transitive:
Let\:\left ( P_{1}, P_{2} \right ) , (P_{2}, P_{3})\: \epsilon \: R
P_{1} \text{ and } P_{2}\: have \: the\: same\: number \: o\! f \: sides
Also\: P_{2}\, and\, P_{3}\: have\: the\: same\: number\: o\! f\: sides.
P_{1}\, and\, P_{3} \: have \: the\: same\: number\: o\! f \: sides.
(P_{1}, P_{3}) \: \epsilon \: R
R is transitive.
Therefore, R is reflexive, symmetric and transitive.
Hence, R is an equivalence relation.
The elements in A related to the right-angle triangle (T) with sides 3, 4, and 5 are those polygons that have 3 sides (since T is a polygon with 3 sides).
Hence, the set of all elements in A related to triangle T is the set of all triangles.

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question