Check sibling questions

Ex 1.1, 13 - Show that R = {(P1, P2): P1 and P2 have same - Ex 1.1

Ex 1.1, 13 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.1, 13 - Chapter 1 Class 12 Relation and Functions - Part 3


Transcript

Ex 1.1, 13 Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5? R = {(P1, P2): P1 and P2 have same the number of sides} Check reflexive P1 & P1 are the same polygon So, P1 & P1 have the same number of sides ∴ (P1 , P1) ∈ R So, R is reflexive. Check symmetric If P1 & P2 have the same number of sides, then P2 & P1 have the same number of sides, So, if (P1, P2) ∈ R , then (P2, P1) ∈ R ∴ R is symmetric. Check transitive If P1 & P2 have the same number of sides, and P2 & P3 have the same number of sides, then P1 & P3 have the same number of sides, So, if (P1, P2) ∈ R & (P2, P3) ∈ R, then (P1, P3) ∈ R ∴ R is transitive. Since, R is reflexive, symmetric and transitive. Hence, R is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5? R = {(P1, P2): P1 and P2 have same the number of sides} Here, P1 = T, So, (T, P2) are in relation R So, T & P2 have same number of sides. So, P2 has 3 sides. So, P2 is set of all triangles Hence, the set of all elements in A related to triangle T is the set of all triangles.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.