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  • 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.

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